People often ask "What is the probability that cryonics will work?"
Arthur C. Clarke said "at least 90%".
The analysis given here, discounting dystopian futures, assuming a good cryopreservation, and assuming Molecular Nanotechnology (MNT) is developed more or less as expected, supports a probability of success for cryonics of 85% or higher, in line with Arthur C. Clarke's 1989 estimate.
For those who find this hard to believe, first consider the growing literature in support of cryonics. This literature includes the demonstration that memory in lower organisms survives vitrification, the successful vitrification and revival of a rabbit kidney, various papers showing good ultrastructural preservation following vitrification, or recovery of function, and the like, as well as review papers explicitly addressing the technical feasibility of cryonics, and review papers showing the feasibility of molecular nanotechnology and nanomedicine.
Then, consider the fact that there are no scientific or technical arguments against cryonics. This remarkable fact simply reflects the observation that (a) there is evidence that current cryopreservation procedures do not cause information-theoretic death, and no evidence that they do cause information-theoretic death, and (b) the development of molecular nanotechnology not only appears feasible, but inevitable. Given (a) and (b), then cryonics will work, barring unexpected problems (nuclear war, accidents, ...).
Had you asked in 1940 if flight to the moon was possible, you'd likely have been told "no". If asked why, a typical answer was "because there's no air to push against in space." This scientific-sounding objection was infamous among knowledgeable scientists, and was the basis for the New York Times 1920 editorial denouncing Robert Goddard.  It was retracted on July 17th, 1969, one day after the launch of the Apollo 11 spaceflight. 
Arguing that future capabilities are unlikely or even impossible based on (a) present inability and (b) confusion about basic science, is quite common. It happened with heavier than air flight ("...The demonstration that no possible combination of known substances, known forms of machinery and known forms of force, can be united in a practical machine by which man shall fly long distances through the air, seems to the writer as complete as it is possible for the demonstration of any physical fact to be." Simon Newcomb, 1901), with railroads ("It is far from my wish to promulgate to the world that the ridiculous expectations, or rather professions, of the enthusiastic speculist will be realised, and that we shall see them travelling at the rate of 12, 16, 18, or 20 miles an hour: nothing could do more harm towards their adoption, or general improvement, than the promulgation of such nonsense." Nicholas Wood, 1825), with radio ("De Forest has said in many newspapers and over his signature that it would be possible to transmit human voice across the Atlantic before many years. Based on these absurd and deliberately misleading statements, the misguided public...has been persuaded to purchase stock in his company..." prosecuting attorney, 1913, against Lee de Forest), and, indeed, with every invention of any merit that has ever been made.
Arguments that cryonics is "unlikely" to work are similar, in that they are based on erroneous assumptions about the nature of the problem and the capabilities of future technology.
If we are to obtain insight into the actual chances that cryonics will work, we must adopt a framework for considering the problem which lets us step outside the constraints imposed on us by our existing technology, and consider rather the fundamental constraints imposed by the laws of physics as they apply to the problem that we face. That is, before considering whether cryonics will work, we need a conceptual framework within which it is possible to make informed statements about whether future technologies might (or might not) be able to revive cryopreserved patients.
Our framework is straightforward: we assume that information-theoretic death must be prevented until such time as future medical technology is able to restore you to good health. If information-theoretic death occurs before a medical technology able to revive you is developed and applied, then you die. If a medical technology able to revive you is applied before information-theoretic death occurs, then you live.
1) information-theoretic death might occur:
2) Technology to revive you must be developed and applied before information-theoretic death occurs.
This framework is intended to provide independent probabilities, so that multiplication of the probabilities can be used to draw conclusions about the overall probability of success. It is easy to create "independent" variables that are in fact highly correlated. For example, someone might argue that for cryonics to succeed, (a) civilization must survive (b) your cryonics organization must survive and (c) someone must have the resources to revive you. All three of these variables are highly correlated, as the survival of your cryonics organization implies both that civilization has survived and that it is quite likely that the resources to revive you are available. Multiplying these three "independent" variables together will produce an erroneously low overall probability of success.
Even in our case, a patient with dementia could suffer a heart attack, not be found for a week, be cryopreserved anyway, remain cryopreserved for so long that background radiation destroys their brain, after which civilization collapses resulting in their premature thawing. That is, items 1(a), (b), (c) and (d) are largely but not entirely independent. However, the case described, and variations on it, seem unlikely to significantly influence our estimated probability of success.
A brief summary of these risks (with a few links to further reading) follows.
Item 1(a) poses a risk that might very roughly be estimated as somewhere in the 10% range. Most people suffer legal death because of a heart attack or cancer. Perhaps the most significant risk of this type is caused by deterioration of the brain prior to legal death from neurodegenerative diseases (e.g., Alzheimer's, Parkinson's disease or other dementias). Accidental damage to the brain (e.g., as in the case of Phineas Gage) would also adversely influence this risk.
Data on the likely prevelance of such pre-mortem dementias is available from the medical literature. "For Alzheimer’s, the estimated lifetime risk was nearly one in five (17.2 percent) for women compared with one in 10 (9.1 percent) for men." The definition of Alzheimer's used was "moderate to severe disease as well as symptoms lasting a minimum of six months." Alzheimer's "accounts for an estimated 60 to 80 percent of cases" of dementia. Quoted from the 2011 Alzheimer’s Disease Facts and Figures . We can reasonably expect that the technology required to revive a cryopreserved patient and restore them to health will be able to reverse dementia, but associated amnesia caused by loss of the actual memory (rather than damage to memory retrieval mechanisms) would not be amenable to repair regardless of advances in technology. The extent of such irreparable memory loss (as opposed to damage to retrieval mechanisms) is not known at this time. In cases of advanced dementia with significant damage to the brain it is reasonable to expect that such irreparable memory loss would be extensive.
Overall risk of dementia prior to cryopreservation might range from little more than 10% to almost 30%, with the actual memory loss from such dementia itself being quite variable. Mild dementia caused by damage to neuronal mechanisms responsible for retrieval of the memory trace that left the memory trace itself relatively undamaged could be fully reversable by application of appropriate advanced technology. Severe dementia that destroyed the memory trace itself could not be reversed by any future technology. We cannot, at the present time, distinguish reliably between these two possibilities in most cases. Arbitrarily assigning a 50% probability to the risk that symptomatic dementia has in fact destroyed the underlying memory trace itself leaves an overall risk of significant memory loss from dementia of from 5% to 15%, or an average of ~10% with substantial uncertainty and variation between men and women. In men, this risk might range from almost negligible if we assume that the memory trace is preserved except in the most severe cases of dementia to a high of ~15% if even mild dementia causes loss of the memory trace. In women, the corresponding range is negligible to ~28%.
This analysis neglects the probability that medical technology in the next few years will find ways to reduce the risk of Alzheimer's. It also begs the question of how bad it is to suffer a "significant memory loss". If you had the option of brain surgery to cure a disease, but the surgery had a 10% risk of "significant memory loss" would you tolerate that risk? If the surgery offered complete recovery of all your mental faculties, but you had some degree of permanent memory loss that forced you to "relearn" some basic facts about yourself, how much damage would this do to you? How much memory loss would you accept before deciding that "significant memory loss" was "unacceptable memory loss"? The answers are likely to vary widely from person to person.
Item 1(b), the risk that information-theoretic death occurs when you are cryopreserved, depends heavily on the circumstances of your cryopreservation. While severe cases (unattended death followed by many days of deterioration prior to discovery) would seem likely to result in information-theoretic death, shorter periods (likely extending up to 16 hours) should pose a much smaller risk. Short delays (cryopreservation under favorable conditions) would seem unlikely to pose a significant risk of information-theoretic death. Long-term memory appears to be stabilized by morphological changes at synapses. Synapses are relatively large on a molecular scale. A "typical" synapse might be one cubic micron. One micron is 1,000 nm (nanometers). A cube with 1 micron edges would have a volume of 1,000 nm x 1,000 nm x 1,000 nm or 1,000,000,000 cubic nanometers. Each cubic nanometer of diamond has 176 carbon atoms in it, so a single cubic micron can hold 176,000,000,000 carbon atoms. If 99% of that space is left empty, the remaining 1% can hold 1,760,000,000 carbon atoms, or 1.76 billion carbon atoms. This many atoms would be sufficient to build a small medical nanorobot, complete with an on-board nanocomputer, effectors, sensors, power, and communications system. A single synapse is an enormouse molecular machine. Synapses have a presynaptic terminal, a synaptic cleft, a postsynaptic terminal, dozens of proteins governing the synaptic vesicles in the presynaptic terminal which contain neurotransmitters, complex molecular machinery to cause incoming nerve impulses to release neurotransmitters into the synaptic cleft, neurotransmitter-activated channel proteins in the postsynaptic terminal, along with other structural proteins maintaining its integrity. After cessation of heartbeat and circulation synapses retain their integrity and identifiability for days when examined under light and electron microscopes. 
The assumption that you will be cryopreserved under reasonable conditions is perhaps the most open to question. Besides logistical issues, the wishes of those who elect cryopreservation can be and have been deliberately thwarted by relatives, medical personnel, coroners, or others. As the legal, medical and social standing of cryonics improves, these risks will decrease, but they will likely remain significant for some time. Those who have most clearly and most publicly stated their wish to be cryopreserved are least likely to encounter cryopreservation injury from this cause. Those most vulnerable are those who are not in routine communication with other members of the cryonics community, those who have not clearly informed their doctor and any medical personnel they might encounter about their wishes, those who make a habit of concealing their wishes, and those who have chosen someone hostile to cryonics or simply indifferent to cryonics for a power of attorney or other legally important function. Make sure no one in a position to block your cryopreservation would benefit financially from such an action.
The wealthy, terminally ill cryonicist with hostile relatives (or any relative or "friend" who feels they "should" receive a substantial part of your estate) who has left substantial sums that do not go to those relatives, particularly if significant sums go to cryonics-related purposes, should take extreme precautions. It is prudent to consider leaving a significant portion of your estate to your relatives, even if that is not your preference. If they receive nothing, they have nothing to lose by taking legal action. Some jurisidictions commonly alter Trusts after the fact for reasons unrelated to the wishes of the decedant: avoid such jurisdictions. Sadly, experience shows that it is prudent to control access to your hospital room or sick bed. Make sure that neither hostile relatives nor their attorneys can gain access to you. If such visits must be allowed, then neutral witnesses should be present, preferably with video cameras, who cannot be bullied by an aggressive attorney. As your mind deteriorates you might say or sign almost anything, and if you are alone with hostile relatives they might claim you said or signed almost anything regardless of what actually happened.
Even in cases where relatives cooperate fully, logistical and other issues can cause delays that reduce the quality of the cryopreservation. When compared with research work aimed at developing cryopreservation protocols that are fully reversible using today's technology, the delays that can sometimes occur during such cryopreservations might raise questions. However, when viewed with the criterion of information-theoretic death in mind, it is reasonable to expect that most of these cryopreservations will result in favorable outcomes. 
The highest quality cryopreservations seem likely to occur when terminal members move to a hospice near Alcor prior to legal death.
Item 1(c) can reasonably be summed up as "Your cryonics organization fails, for whatever reasons, to carry out its mission." Alcor was founded in 1972, and its continued existence and growth is a favorable indicator. Pragmatically, the more people who support cryonics the less likely that this failure mode will occur. Some argue that civilization is likely to collapse within the next century (and describe a diverse menu of possible causes). It is difficult to assign probabilities to these dystopian futures. Those who seriously believe that we are all doomed are invited to watch television or otherwise amuse themselves. Those of us who think humanity has a future will continue to make plans based on this assumption. Alcor appears stable and the people involved are dedicated to carrying out its mission. Barring dystopian catastrophes, the probability that Alcor will fail seems quite small.
Item 1(d) is unlikely to occur in less than a few thousand years, as the only significant source of damage inside a stainless steel Dewar of liquid nitrogen protected from light and mechanical damage is background radiation of ~0.1 rads/year. It would take about 6,000 years to accumulate a lethal dose of 600 rads by today's standards (see the Alcor FAQ entry and Merkle's cryonet posting on this subject and the comments by a cryobiologist).
This failure mode can reasonably be ignored, as it seems unlikely that it will be necessary to remain cryopreserved for more than 6,000 years.
Item 2, the failure to develop the required technology despite the passage of multiple centuries, seems unlikely. More specifically, published analyses strongly support the feasibility of both nanotechnology and nanomedicine. Given sufficient time and the non-collapse of civilization, they should both be developed.
As nanotechnology, nanomedicine, and the ability to revive cryopreserved patients who have not suffered information-theoretic death are based on the foundation provided by our understanding of physical law, and as that understanding, as it applies to the physics and chemistry that is relevant to human biology, biochemistry and neuroscience is highly unlikely to change in any significant fashion, let alone change in a way that would undermine the feasibility of cryonics, we can reasonably conclude that the development of the relevant technologies is primarily a matter of time. There are no fundamental issues of physics that stand between us and the recovery of the information present in the cryopreserved brain of a patient who has not suffered information-theoretic death, and there are no fundamental issues of physics that prevent us from restoring the atoms in a cryopreserved human brain to an arrangement that corresponds to that person following their full and complete recovery.
Not only are these technological issues clearly feasible in principle, implementation pathways have been outlined and specific implementation strategies have been proposed and analyzed. Development of the relevant technologies is now well underway. The 4th Quarter 2008 issue of Cryonics magazine discusses the application of MNT (Molecular Nanotechnology) to cryonics. Feynman's classic talk There's Plenty of Room at the Bottom is required reading for anyone interested in this subject.
Discounting dystopian futures, assuming at least a reasonable quality of cryopreservation, and assuming that MNT is developed more or less as expected, the probability of success seems quite high - likely exceeding 85%. The major risk is pre-existing advanced dementia prior to cryopreservation, particularly Alzheimer's.
There is an extensive published literature supporting the feasibility and likely development of MNT. The probability of its successful development at some point in the future is extremely high.
The quality of cryopreservation varies substantially depending on a number of variables, many of which individual members can influence. Perhaps most significantly, make sure you have discussed your wishes with family members, medical personnel, and others who you routinely work with, and that they know what to do when the time comes. Also make sure that your legal affairs are in order, and again, make sure that everyone knows what to expect when the time comes. Make absolutely certain that those who will have legal power over your affairs support your decision and will carry out your wishes. Failure to carry out any one of these steps can, and has, caused havoc with what otherwise seemed like perfectly reasonable arrangements.
Claims that cryonics is "impossible" or "unlikely to work" are not supported by any published technical articles or analyses and are uniformly based on gross misunderstandings or misrepresentations of basic aspects of cryonics.
Many of the fundamental technical issues are discussed in The Molecular Repair of the Brain.
1. 2011 Alzheimer’s Disease Facts and Figures
2. Morrison and Griffin said "We find that both rat and human cerebellar mRNAs are surprisingly stable under a variety of postmortem conditions and that biologically active, high-molecular-weight mRNAs can be isolated from postmortem tissue. ... A comparison of RNA recoveries from fresh rat cerebella and cerebella exposed to different postmortem treatments showed that 83% of the total cytoplasmic RNAs present immediately postmortem was recovered when rat cerebella were left at room temperature for 16 h [hours] postmortem and that 90% was recovered when the cerebella were left at 4 degrees C for this length of time .... In neither case was RNA recovery decreased by storing the cerebella in liquid nitrogen prior to analysis. ... Control studies on protein stability in postmortem rat cerebella show that the spectrum of abundant proteins is also unchanged after up to 16 h [hours] at room temperature...." Johnson et al. in "Extensive Postmortem Stability of RNA From Rat and Human Brain" found that postmortem delays of as long as 48 hours "...failed to reveal degradation of the specific rat brain mRNAs during the postmortem period." They also said "We find no effect of postmortem delay on RNA quality in both rat and human."
Morrison and Griffin. "The isolation and in Vitro translation of Undegraded Messenger RNAs from Human Postmortem Brain," by Marcelle R. Morrison and W. Sue T. Griffin, Analytical Biochemistry 113, 318-324 (1981).
Johnson et al. "Extensive Postmortem Stability of RNA From Rat and Human Brain," by S. A. Johnson, D. G. Morgan, and C. E. Finch; Journal of Neuroscience Research Volume 16, pages 267-280, 1986.
3. “Procedural and declarative memories differ dramatically. They use a different logic (unconscious vs. conscious recall) and they are stored in different areas of the brain. Nevertheless, these two disparate memory processes share several molecular steps and an overall molecular logic. Both are created in at least two stages: one that does not require the synthesis of new proteins and one that does. In both, short-term memory involves covalent modification of preexisting proteins and changes in the strength of preexisting synaptic connections, whereas long-term memory requires the synthesis of new proteins and the growth of new connections. Moreover, both forms of memory use PKA, mitogen-activated protein kinase (MAPK), CREB-1, and CREB-2 signaling pathways to convert short-term to long-term memory. Finally, both forms appear to use morphological changes at synapses to stabilize long-term memory.” Synapses and Memory Storage by Mayford M, Siegelbaum SA, and Kandel ER. Cold Spring Harbor Perspectives in Biology, April 10, 2012, page 10.
4. "We can thus suppose that the volume of each synapse plus its uniquely associated structures will average around 1 μm3." The Bounded Brain: Toward Quantitative Neuroanatomy, by Christopher Cherniak, Journal of Cognitive Neuroscience, Volume 2, No. 1, pages 58-68. https://terpconnect.umd.edu/~cherniak/JCN_90.pdf
5. "A reasonable design for this sort of replicator will likely include several assembler arms and several more arms to hold and move workpieces. Each of these arms will add another million atoms or so. The other parts - tape readers, chemical processors, and so forth-may also be as complicated as assemblers. Finally, a flexible replicator system will probably include a simple computer; following the mechanical approach that I mentioned in Chapter 1, this will add roughly 100 million atoms. Altogether, these parts will total less than 150 million atoms. Assume instead a total of one billion, to leave a wide margin for error." Engines of Creation by K. Eric Drexler (1986).
6. For further consideration of the kind of damage required to cause information-theoretic death, see Cryonics, Cryptography, and Maximum Likelihood Estimation.
7. Topics of the Times, (The New York Times, 13 January, 1920, p. 12, col. 5) "That Professor Goddard, with his "chair" in Clark College and the countenancing of the Smithsonian Institution, does not know the relation of action to reaction, and of the need to have something better than a vacuum against which to react--to say that would be absurd. Of course he only seems to lack the knowledge ladled out daily in high schools."
8. The New York Times, July 17th, 1969. “Further investigation and experimentation have confirmed the findings of Isaac Newton in the 17th century and it is now definitely established that a rocket can function in a vacuum as well as in an atmosphere. The Times regrets the error.”