The other strange thing I noticed occurred last night; I decided to play a rather old game (Sid Meier's Colonization), which requires that I set the monitor to 256 colors. I played for about 8 hours with no problems (with iTunes running in the background), something I haven't been able to do with any other program so far. Same thing this morning: no detectable problems playing the game.
The computer always restarts fine, it's mostly just annoying, but I'd like to get it fixed, or at least get an idea what's wrong, before it gets any worse.
(For reference, it's an Apple G4 eMac, about 2 years old at this point. It had the display and battery replaced in February)