Suppose I want to compare groups A and B on 5 variables: age, education level, blood pressure, brain volume, and glucose level. Given that the assumptions are met, I will use the 2 sample t-test to make 5 comparisons. In this case, do I have to correct for multiple testing? What if I wanted to compare the groups on 10 variables? Or 20? Under what condition should I correct for multiple testing?
It's ultimately a matter of taste. How conservative do you want to be? What kind of error rates are you after—are you okay with a type-I error rate of .05 for each comparison, or do you want a rate of .05 for the whole set of comparisons, or something else?