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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 ...

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This article by Whelan (2010) is one of the best introductory papers I've found on the subject. Normalization is covered quite clearly and extensively, including the caveats and "gotchas". References Whelan, R. (2010). Effective analysis of reaction time data. The Psychological Record, 58(3), 9.

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My impression is that, recently, a consensus began to form recently that RTs should be transformed to satisfy model assumptions. This is especially true when data is analyzed with mixed models instead of ANOVAs. Concerning the stability of effects under different transformations, you may find this paper interesting: http://web.uvic.ca/psyc/masson/KMR10.pdf

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