My eMac freezes constantly. (At first in WoW, then in everything)

Sounds an awful lot like your graphics chip is dying, which is a bummer since it's integrated in the eMac and not exactly easy to replace. It could be an OS issue, but that seems unlikely based on the sympoms.

Two things to try, if you haven't already: Break out the discs that came with it and run the Hardware Test disc. This will do a quick and dirty check, and if IT reports errors, then you know for sure it's hardware, and it'll probably tell you what piece, specifically. If it happens to be under warranty (I'm guessing no?), then get it fixed. Even if that gives you a clean bill of health, it doesn't mean the hardware is ok, just that it can't detect the problem.

If, however, you don't get any hardware errors while running that check, you could try reinstalling the OS and see if it helps. Probably not, but if you're going to have to get it fixed or call it dead anyway, it's worth a shot.

Again, this is assuming it's not still under warranty. If you are, run the hardware check disc, then call Apple regardless of what it tells you (if it gives an error, that'll just make your life easier on the phone with them).

Sounds to me like you're having "Distorted Video" problems, so I'll bet your're covered. At the very least, they can't blame you for bringing it in thinking you do based on the symptoms, even if it turns out to be something totally unrelated.

try making a new user to make sure it's not something you've "done".