Many times in sample size calculation I observe that a sample size of below 10 is caculated. Most often this happens when we calculate sample size using variables reported in Mean+/- SD. What should be the minimum sample size in such cases.
Diferent methods can be used depending on what are you looking for (compare means, calculate a proportion, etc), the type of the study, and the information available in the literature. In my opinion there is not a overall rule.
The answer depends on: (a) your research goal(s); (b) the size and nature of the population; and (c) the variable(s) of interest.
If your chief concern is precision of parameter estimates (for example: What is the proportion of adults in Florida who have melanoma?)j, then there are numerous sources that can assist you in determining what sample size will be needed to estimate the parameter of interest with the desired precision (and with some degree of tolerable risk of being wrong).
The classic text, Sampling techniques by William G. Cochran, is hard to beat as an introduction.
If your concern is that of conducting hypothesis test(s), and you want to determine a suitable sample to assure some level of statistical power to detect whatever effect size magnitude you consider worthy of detection with some specific test run at an alpha level of your choice, then software such as G*Power (freely available, at http://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower.html) can help you figure this out.
In general, though, I'd be very skeptical of advice that 10 cases (or fewer) is a satisfactory sample for anything other than a pilot study.