This has been happening to me on and off for a while, and recently started happening to a friend of mine as well. I'll list my stats (don't know hers off the top of my head) and throw out what I believe to be the most likely culprits. I can't afford to spend on something that isn't a pretty sure-fire solution though, as I am dirt poor.

This is likely a hardware issue, it happens to me in all environments. It seems to be triggered by heavy load or by certain types of load on the computer; specifically video games and video.

My spex:
ASUS P5K-E w/Wifi mobo
2.66 Core 2 Duo
4 gigs of RAM
geForce 8800gts
120gig WD
360gig Seagate

The issue:
It just shuts off sometimes. If it does, it won't turn back on unless I wait a few minutes. There doesn't seem to be a TON of rhyme or reason to this, except that it does seem more frequent when under heavier load, as mentioned.

Most likely culprits imo:
Two things I've noticed similar between my setup and my friend's: the geForce 8800gts and the fact that at least one of the PSU's rails (5v for mine, +12 for hers) is more than 5% off consistently. For me, it's the 5v running at about 5.52, which is more than 10% off if you don't care to do any math. Her 12v is running at 11.3, which is JUST past the 5% threshold.

Other than that, I can't think of anything really. My PCU was heating up so I threw an extra fan in there, and eventually started shutting off sensors in the BIOS in order to isolate the issue. The RAM is quite new, so it's probably not bad.

Things I've tried or am about to try:
Turned off almost all sensors, disconnected nonessential drives. If push comes to shove I'll disconnect ram sticks 2 at a time, flash my BIOS on the very offhand chance that an old version might cause some problems with hardware, and then... I don't know, start borrowing parts till it works?

Is there a way to check what happened to cause a bad shutdown, maybe give me an error code I could google? BIOS post message maybe? Is this a common issue? Anyone have experience with this sort of thing?