Apparently, that my XBox 360 lasted from the day it went on sale until today is unusual. I was negotiating a turn in Forza 2 and the system froze. Rebooted, it froze during race startup. Rebooted, and now it's "the Red Ring of Death."
According to this site, I can expect to be told that it will cost $140 to get a refurbished replacement, but if I bitch I'll get 25% off. Oh well, maybe the replacement will be quieter -- there's no way the fans I had on this thing were up to spec.