My computer (an iMac) shuts down, then restarts by itself about 15 seconds later. Any ideas?
oh… this is when I shut it down, that is
I know this will read as a rather flip answer, and I apologize in advance, but I’d recommend calling Apple tech support.
It may be a wait because [insert Mac insult of choice], but they should/had better know what can be done.
I can’t resist…
Are you shutting down? or restarting?
Also, check your power settings if that’s really not the case…
In the Control Panels, under Energy Saver, you’ll find settings for shutting down and starting up your mac, try a few of the Control Panels, you might find it’s something there, really simple after all.
After all, it’s a mac, how hard can it be? 
Hah. My HP Pavilion, with the new, improved Windows ME, is obviously YEARS ahead of your silly iMac. My machine reboots ITSELF. So there.
Often in the middle of playing Diablo.
are you clicking on the button marked <restart>?
How long ago did this start?
Did you try rebuilding the desktop file yet?
What is your quest?
What is your favorite color?
Oh, this is nothing! My computer shuts down all the time (an old Gateway). But that’s not all! It completly shuts down, then the speakers blare the phrase “Run! Run like hell!” over and over again for about five minutes before the ungodly thing restarts.
No joke.
I think it’s trying to kill me…
Probably not related, but many times when a computer just shuts down it’s a processor problem. It overheats, and it will come back up after it cools down. I just had this problem, and some thermal grease to the back of the processor’s heat sink solved the problem.
Unplug it?
So the question was actually, ‘computer restarts after shutdown’? Maybe it has a virus? Why don’t you just turn it off? You know, hit the power switch. Or unplug from wall, If after doing that it restarts by itself, call me, I want to buy it.
Conctact Apple there is a known problem with faulty power switchers on some iMac’s and Cubes
MannyL would know this- I used to work where he does.