Hi EAS,
There isn't a universal rule of thumb because it depends on how large your effect size is and what alpha you are using...etc A rule of thumb you sometimes here is that each group should have at least 30 people, but that is assuming there aren't additional covariate and probably at least medium effects. Your best bet is to use a tool like g*power to calculate your power based on the size of your groups:
Here is a link to g*power:
http://www.psycho.uni-duesseldorf.de/abteilungen/aap/gpower3/
I have been looking for a reference that gives some guidance for how small can the sample size of a dummy variable be. For example, we have a category for religion that yields many categories, with several only representing 4 or 5% of the total sample. We want to create dummy categories for the different religion types to include in multivariate regressions. At what point, do we combine some of the categories into one? Is there a general rule? Thanks