UPDATE: Got the call today from the service center and was told that my power supply was defective....

So, I have not had a problem with this since resetting the PRAM. It looks like that was the issue for this particular instance. My advisor is having the same problem, but it is much more frequent than mine was--up to like every 15 mins or so. I gave her the instructions on how to reset the PRAM, I'll let you know if it works. I'm going to guess that hers is a power supply problem. Oh, and it's not an intel mac, its the version right before it.

A bit late to the discussion, but need similar help
 

I realize this topic was back in 2008, but I am having the same problem today. I have a 20" Intel duo 2 iMac that has spontaneouly shut off twice. At least I thought it had. WHen it happened today I put my hands on the machine and my ear against it and it was not off. Just the screen was black. It was like it had actually gone to sleep, but could not be woken up. I finally just held the power button twice until it restarted. Then I came here to check the problem out. I looked in the system log as suggested (had to google how to do that) and discovered something very weird. I have an application called Alarm Clock that I use every day to wake me up. It's set for weekday wake-ups and a Sunday wake-up. Well, the system log had this report from the moment the screen went black:

6/5/11 11:32:13 AM Alarm Clock[1709] kIOMessageSystemWillSleep

6/5/11 11:32:13 AM [0x0-0x93093].com.digitallity.alarmclock2[1709] 2011-06-05 11:32:13.378 helper[9648:903] Adding power event: 2011-06-07 06:25:00 -0500

What's weird is that it says an event is scheduled for 6:25 on June 7, which it is, but that is a Tuesday. There is the exact same event scheduled for Monday June 6 that isn't mentioned. Somehow, it seems that Alarm Clock looked at the upcoming Tuesday event and then put the computer to sleep - so deeply it wouldn't wake up.
Is that what it looks like to you guys? Should I uninstall Alarm Clock?