Should raw response time data be transformed?
You can transform RT, i.e., by log(1/RT). This makes the distribution roughly normal.  The problem is that you don't usually run the ANOVA on the RT values collected at each trial, but on the average for each participant. So the distribution across participants need to be normal. A trick is to transform the single RT values, calculate the mean for each participant and condition, and then transform the value back with the inverse.

Alternatively, you can run ANOVAs without corrections if you use the appropriate one (i.e., normality not assumed... this will lead to oddly-looking DOF with decimal values).