This started happening to me too. Bought my MacBook in the last week of May. Base model with 1GB upgrade. Had one or two mysterious shutoffs about halfway through June, but then they started happening a few times a day.
After a few suggestions from Apple Care, I tried the Apple Hardware Test. The machine would very reliably shut off during the Memory Test part, but only if I had the extended test box checked. So I figured it was the memory, and the guy at the Apple store agreed. He replaced it, and the hardware test passed in the store, twice. I got home, and after using it less than an hour, it shut off twice.
Back to the Apple store, a different tech guy, is reluctant to just replace the thing without having witnessed the problem. I can understand that. But he goes in the back, and I guess talks to a manger or Apple or something, and comes out ready to replace the machine. New MacBook on the table next to my old one, firewire cable between them, and the old one booted up in target disk mode. Four attempts at data migration failed; it would power off. Which means it's definitely not a software issue. On a whim, the guy tried once more with the old one running on battery, and the data migration succeeded.
I've had the replacement for five days. So far no issues, and this one doesn't moo (unlike the last one). Looks like the only fix for this issue is to replace the logic board, or a full machine replacement.