A few months ago I bought a shiny 20" iMac. While the initial impression was good, I was not happy after the trouble I had installing Leopard and certain incompatibilities it brought.
Just when it seemed things were settling down I've got the system just dying on me after opening a large (120MB) PDF file. The screen turned black and then the system rebooted spontaneously. Another computer was on at the same time and it did not experience any problem, so I do not think that was because of a power spike.
Today, when I started the system there was a multilingual message in a centered dark square telling me to press the power button for several seconds to shutdown the system (neither the keyboard or the mouse worked). I have never seen that image before (but I failed to take a photo), it contained the message in Japanse too. It happens to be an OS X kernel panic.
When I powered on the system again I heard the welcome sound and next two beeps and then three beeps that repeated over and over again. It did not sound good. A quick check on the net (using other computer, of course) showed that 2 or 3 beeps signal RAM memory trouble (mine is the original RAM that came with the system and because of the cool and compact format of iMac is not user serviceable).
I removed the computer power cord for some seconds and then I connected it back to try again: No changes, same sequence of sounds; no joy.
Having nothing to lose I removed the power cord again and I applied some of my frustration through my hands (i.e. more than gentle taps to the system). After reconnecting the power the system booted up as normal. My guess is that the RAM is not properly seated on the socket. I'll be paying attention to see if something weird happens again.
Now I'm going to hunt for some memory test software.
Update: Thanks to Jesus coments (and this page) I realized I was wrong: My iMac does have two memory slots that are easily accessible by the user by removing two screws on the bottom part of the screen. Not sure the trouble was caused by memory though, as several diagnostic attempts gave no indication of memory faults. Anyway, if the problem happens again now I know I can access the system's RAM memory.