I recently bought Gainward 8800GTS 512 BLISS. Card worked for 30 minutes, and after I ran Crysis I got BSOD. Now I see red squares, green dots and other artifacts just after pushing the power button. Everything gets back to normal when I let the card cool down (about hour). But lanuching any 3D application cause crash and artifacts appear again.
I don't think its a PSU problem - it worked well with Tesla C870 (which is more power consuming than 8800gts as I know) and GF8600GT, those cards were used simultaneously in multi GPU CUDA apps.
I tried many driver versions on Windows XP x64, Vista x64 and Linux x64. I also tried to turn fan to 100%, GPU temperature was about 40 C when I ran simple 3D app, after few seconds system crashed but there were no temperature increment.
I also tried to connect different monitors (digital and analog) - didn't make a change.

My specs :
Core Quad Q6600 G0 2.4 GHz no OC
Abit IP35 Pro no OC
Gainward 8800GTS 512 BLISS no OC
Chieftec 560W PSU
3x WD 320 GB
Coolermaster Dominator CM-690 case

Any idea what is happening ?

I think that your card is overheating. Maybe not core, but memory chips. See if you can open your case or direct some air at it.