I have had my 360 now since around New Years Day, I can't remember exactly...
It has froze up or shut itself off on me at least once per week since I have owned it...mostly freeze ups, I think there was only 1 shut down.
Now, I have owned: Atari 2600, ColecoVision, Nintendo, Sega Master System, Sega Genesis, Playstation, XBOX & PS2. If I add up all the freeze ups/shut downs on all of those systems that I can remember, I don't think it totals what my 360 has done in the last 9 weeks. 9 f'n weeks. I fear that my unit will soon stop working completely and I'll have to jump through hoops to get it fixed.
I was going to go the PS3 route until the itch to play Oblivion on my 56" TV was too great and mentioned one day to my wife, "I think I'm gonna get a 360 before a PS3...". Within 2 days, she came home with said console/game. (she rocks, btw).
Just thought I'd share my little experience with this system...it does seem to be pretty unreliable.