defaults write NSGlobalDomain KeyRepeat -int 0
Then log out and log in again. The fastest setting obtainable via System Preferences is 2 (lower numbers are faster), so you may also want to try a value of 1 if 0 seems too fast. You can always visit the Keyboard & Mouse System Preferences panel to undo your changes.
You may find that a few applications don't handle extremely fast keyboard input very well, but most will do just fine with it.
[robg adds: We originally ran a very similar hint back in 2003. However, that hint had the order of the values reversed, and made the change via editing a preferences file instead of via a defaults write command. So I felt it worth re-running this version as it's simpler and more correct. If anyone knows what service to restart to skip the logout/login step, please comment.]