I recently purchased the $200 (after rebate and coupon) sapphire 5870 at newegg.
I got the GSOD. I updated everything I could (bios, drivers, re-installed windows, etc). Nothing helpped.
I RMA'd to Sapphire (since the card had a rebate and I already cut out the UPC). Got a replacement and still get the GSOD.
I have researched around the Internet and some people seem to think that the GSOD issues started to reappear in drivers 10.10 and onward.
I have since installed 10.09 drivers and have not had a single GSOD. I only did this yesterday, so I'm not in the clear just yet.
Sometimes instead of the GSOD, I would get the "Display Driver Stopped Resonding" error and windows reloads the driver. This also appears to be happening on some 6xxx cards as well.
http://forums.amd.com/game/messageview.cfm?catid=260&threadid=144813
I suggest trying 10.09 drivers. If that doesn't work, RMA and see if a replacement fixes it.