So called "anecdotal cases", individual stories of recovery, are usually derided by the mainstream as unscientific, if not the hallmark of quackery. They are also a form of evidence that is particularly prominent in alternative medicine. I believe individual experiences with cancer therapies can be meaningful as evidence (and I also find complete discounting of individual human experience philosophically offensive). I think that there are specific reasons why cases can be meaningful evidence in cancer, even though there there are also serious limitations to cases as evidence.
Most diseases are self-limiting, and/or they often get better without treatment - and this is true even of serious diseases like arthritis and multiple sclerosis. Cancer is different. Spontaneous remission of cancer is an exceedingly rare event. It is also largely confined to a few specific types of types, renal cell cancer, the most common form of kidney cancer, melanoma, a serious skin cancer, certain lymphomas (lymphoma is a cancer of the immune system) and a rare childhood cancer called neuroblastoma. In renal cell cancer, the rate of spontaneous remission has been estimated at about one in 200 cases. For most other cancers it is much, much rarer. So since cancer almost never goes away by itself, if it does go away then (possibly excepting the cancers in which spontaneous remission is 'common') the best explanation is the treatment the patient received.
Even though cancer doesn't go away by itself, in my experience, most claims of benefit from alternative therapies do not pan out on closer examination (or commonly there is not enough information to be able to tell). It is extremely common for cases which sound convincing at first blush to be unconvincing when you get the details.
Consider this example: "Aunt Sally had lung cancer and was told by doctors she would probably not live 2 years but here she is a decade later alive and well - and its all because she used alternative therapy xyz." First, you don't know what other treatment she had - maybe she had surgery and chemotherapy and the odds were bad, but maybe she beat those odds! Second, you don't know what kind of "lung cancer" she had - and don't forget, many people will call cancer metastatic to the lung, "lung cancer," and the type of cancer matters if you are researching treatments for yourself and want to know what might work for your cancer. But even more important, what if it turns out the doctors only thought she had cancer based on an x-ray and there was never a biopsy? What if she never had cancer to begin with? This actually happens from time to time.
An individual case really doesn't tell you much of anything unless the chances are very small that there is another explanation for the seeming success of the therapy. So it is necessary to be sure the person actually had cancer, and actually got better, and that only the alternative therapy could reasonably be said to be responsible for it.
Even though cases can indicate that an alternative therapy has some promise, they do have some serious limitations. Key questions about a cancer therapy, are, "who does it work for?," and "how often does it work?" It is very difficult to get answers to either of these questions from cases alone.
You'd like to know the percentage of people who the therapy works for. This is a fraction - the total number of people for whom it worked divided by the total number of people who tried it (times 100). If you know that a therapy has worked for some people because you have cases, you have at least part of the numerator of this fraction but you know nothing about the denominator so you can't know how often it works. Were these cases a few truly exceptional successes, or are they just typical examples of the therapy at work? Sometimes knowing that there are at least some real successes counts for a lot even if the success rate might be quite low. Often, that's just not good enough because you have better choices. It all depends on your situation.
Most cancer therapies work better for some types of cancer than others - in fact most are quite specific to the type of cancer and would only rarely work on other cancers. It is then very important to know whether a therapy works in your type of cancer. If you have an assortment of a few cases with an assortment of different types of cancers it is difficult to tell which types of cancer it might work best for. Of course, if all the successes are one type of cancer that is a pretty big hint, but that is not usually the case!
Despite these limitations, I do think sometimes you can get something of a feel for how often a therapy works. First, if there are really only one or two cases, then it is possible that despite your careful investigation, they actually were due to a rare spontaneous remission, or a mistaken diagnosis, or some other error. So you need a selection of cases. If the cases are being provided by a clinic, consider how long they have been treating patients, and how many cases there are. If they have treated a great number of people there should be a substantial number of valid cases. It is suspicious if most of the cases are invalid, even if some are valid, since a clinic with real successes should know what a real success actually is! I think it is a very positive sign if within a small group of people who have tried a therapy there are several successes. For instance, if on hearing of Joe's success with supplement xyz, 6 of his friends with cancer tried it and three had remissions from it. The point is that in situations like this, the numerator is small but the denominator is better known. Against a background of other cases and evidence, this is promising. If a therapy is extremely popular then if it really works, there should be lots of valid cases. The lack of valid cases for Essiac posted on Internet forums, despite its great popularity, leads me to conclude it is probably not very effective. Conversely, if a therapy is little known and there are a large number of valid cases that is obviously very positive.
You also have to consider how much "access" you have to cases. A professional would want to review all the films, charts, test results, reports and pathology slides themselves to do a really through scientific review. You won't be able to do that (although once in a while you may find reports where professionals not associated with the therapy have done this kind of evaluation - there are several evaluations of this type for antineoplastons, for example). But you may be able to talk with patients and you may be able to elicit enough information to have a pretty good idea whether the case is valid or not even if you can't be quite as certain as a team of professionals. In some cases, you may find the patient doesn't know enough about their own case for you to be able to draw any conclusion. For some therapies, there might be a brief printed description of cases which sound interesting but without much detail. It is difficult to draw very solid conclusions from such cases even if they sound intriguing. An example of this is the Gerson therapy's promotional literature which features brief descriptions of "Cured Incurables". (Dr. Gerson's "50 cases" presents cases in much greater detail). Although cases do leave a great deal of unknown, they are still evidence and can be weighted with the rest of the evidence for or against the therapy and with the plausibility of the therapy to get an estimate for the promise of a therapy. If the only evidence is cases then the uncertainty in the estimate is likely to remain great. Accepting great uncertainties is part of learning to deal with cancer. Minimizing the uncertainties to the degree possible is part of good judgment and maximizing the odds.