I'm having the same problems with my MacBook 13" randomly shutting down. I detected this before the 10.4.7 upgrade, but it has been happening more often since that upgrade, and it happens alot when running Parallels Desktop (and Windows XP). I have 2GB of RAM, which I installed myself after purchasing it mail-order from RamJet. I could actually get it to shut down without fail when I launched Parallels Desktop and then when Norton Anti-Virus would do its scan. In fact, I had to quickly cancel the scan to keep it running, and then removed Norton Anti-Virus completely, which helped somewhat, but it has now hit me several times this morning when I wasn't even running Parallels Desktop.
AppleCare support was not very helpful. The man I spoke with had never heard of Parallels Desktop, and was asking me whether it had been updated to run on Intel-Macs (uh, it ONLYruns on Intel-Macs). He then suggested the ol' RAM swap routine, which I was going to try next. Anyway, I am now running on a single memory module (1GB), so I'll see if it is stable for the next few days, and if so, swap it out for the other module. If both are stable by themselves, then it has to be something else, I would guess.