My experience seems to be similar to mediathology's problem description.
I have my 27-inch, Intel core i7 iMac plugged into a multi-outlet, switched, surge-suppressor power strip that is plugged into an APC UPS. At night I shut down the iMac and switch off the power strip. The iMac worked well for the first two days.
On the morning of the 3rd day, It would not start, and there was no startup chime. I made several tries: switch off the power strip, wait a while, turn the power strip back on, then press the iMac's power button. Each time, I could hear the HD start spinning and doing several seek operations. After that, nothing happened.
I then did a forced iMac hardware shutdown (press and hold the iMac's power button for 10 to 30 seconds until the iMac shuts down). I heard the HD stop spinning. After a few seconds, I pressed the power button, and the iMac started right up as if nothing had ever happened.
The problem occurred again on the 10th, the 25th and the 34th days. Each time, it showed the same symptoms and the same response to the forced iMac hardware shutdown.
I've called Apple twice. The first tech I spoke with issued a case number and gave me some suggestions to avoid the problem (basically, don't shut down). On the second occasion, the tech insisted on giving me a new case number, and suggested I take my iMac to the nearest authorized repair shop to have it checked.
After the fourth occurrence, I downloaded both of Apple's newly released firmware updates and installed them along with the OS X 10.6.3 update. One of the firmware updates is supposed to address a problem where the screen won't light up. I haven't seen any more details, so I don't know if this problem is related to the not-starting-up problem.
That was nine days ago. I am currently waiting to see if the problem happens again. If not, then good. If it does, I will have to call Apple again, then take it to the service shop (35 miles away).
(Apr. 27, 2010)