How do you decide how many trials to have in an experiment? I'm currently designing an experiment with several conditions - how do I decide how many repetitions / stimuli within each condition?

I know that I can justify sample size with an a priori power analysis...is there any common way to choose how many trials within each of my conditions?

I was using sample size/power as an example of something where there is a particular approach to help decide.....what I am actually asking about is the number of trials i.e. if I have three conditions in my experiment, how many stimuli should I design for each of the conditions?
A power analysis is typically based on the difference in the mean to be detected and the expected standard deviation of the data. The amount of variation in the data (i.e., the size of the standard deviation) typically depends on individual differences in the subjects and measurement noise. The measurement noise depends on a number of things, but in many experiments can be reduced by running more trials. In the minimal risk experiments I am most familiar with, we run so many trials that we reduce the trial related noise to inconsequential amounts. We tend to use wildly inefficient methods for collecting the trials also (our stimuli and response interval are too long, we use multiple intervals, and our adaptive procedures are not optimized).

In order to minimize the data collection/maximize power (and this should not be the only goal) the stopping rule generally cannot be a number of trials, but rather a precision criteria. There are procedures (e.g., ZEST) which can be set up to use a fixed number of trials or a target precision.