I'd like to respond to this thread with ideas from a setup we did use in our lab to measure reaction times. But first off, let me briefly respond to this:
In the CAD/CAM lectures I attended a long time ago, I think I recall hearing that the fastest reaction time humans can manage is measured in hundredths of a second. Fencers were given as an example.
The order of magnitude is indeed right. But the problem we face isn't measuring short reaction times, but precise reaction times. In experimental psychology, we deal with human responses that are highly variable. Mostly because subjects don't necessarily attend to the experiment with care, and, well, we just can't control what's in their head that precisely.
So we want to minimize the variability associated with the reaction times measure. When using the computer, the variability from the human response is added to that of the computer. For us this means that to observe a statistically significant difference between two experiments we'll need the subjects to perform more trials so that this variabilty averages out. That's a loss of time for everyone.
Hence, whatever the average reaction time is (which depends on the task at hand), the problem here is to reduce the variance.
As for the solution we had implemented. We are mostly doing psychoacoustics, so we could use the following trick. A sound card is inherently a very precise piece of hardware temporally speaking. So what we did was using a three channel sound card, two of which send the simuli (stereo), and the last one sending a clic to an arduino (it wasn't an arduino, because they didn't exist at the time, but that's irrelevant). We then had the arduino start a timer that was stopped by a button on the arduino (the subject's response button). The value was then sent to the computer.
The idea is really to have the arduino do the timing, and find a way to send it a "start" signal. In vision experiments, you could imagine doing this by taping a photoresistor to a corner of the screen, which you would light up when the stimulus starts.
I hope this helps.