I did some research because I just got an 8800GT. I wasn't able to find any specs specific to my card, but a comparable BFG card listed at least a 425W power supply with 28A on the 12V rail. My power supply is 500W with 28A on the 12V. It has been running solid for the past week, even when gaming (Crysis, TF2, Portal, etc.).
You don't need a 1000W power supply...somewhere around 500W should do, but make sure the 12V rail has the amps you need. Like I said, 28A was recommended for my card. It can't hurt to get a bigger power supply however. Your computer will only use what is necessary to power the components in the tower. I agree with Tykael though; you are probably better off spending the extra $20 or so on a decent power supply. The cheap ones tend to cause more problems than they solve.
I see people spending like $200 on a power supply these days. I think that's absurd, but I'll spend $50-$60 instead of $20 on a cheap-o that's supposed to be the same.