My mid-2007 white 2.0 Mhz MacBook ran great, until the 1 year warranty period ended. It now overheats and shuts down with annoying irregularity, typically under high CPU activity. (I had a terrible time doing an initial Time Machine backup on a new external HD. Movies are a problem.) I think the problem is the cooling fan(s?) -- it does not work. I think the source of the problem is in the SMC bios. It is quite likely that whatever was wrong started prior to the warranty period expiration but I did not notice it and the Apple Hardware test did not disclose it. The computer runs great 90% of the time, but ....
If you don't have Applecare and your Mac is less than 1 year old, get it! I used to think that if a computer worked for the first 24 hours, it would likely go on forever. That was true with all of the old IBM's that I ever owned or managed, but not with the MacBooks! Check the forums -- there are a lot of 'heat' issues out there. At least with Applecare, (God, I hate to have to say this!) you have a 3 year window to get the 'hidden' problems fixed.