My specs will be at the very end. I have had a total of four graphics cards, AMD Radeon 7750, 7770, 7850, and now the 7950. Every single one of these graphics cards gave me the same issue named as the title. Not until now has it been so extreme, before my screen would go black and go right back to where I was displaying the error. But now, whenever I try to launch ANY game, I get the error. I have tried to change the directory for TdrDelay and no luck, launch Battlefield 3, same error. Minecraft, same error. I have uninstalled and re-installed the drivers so many times it's getting ridiculous. All my system drivers are up to date as well.
Since you have had the issue on multiple cards it needs to be either an OS issue or a hardware issue. The hardware issue would be a bad PCI-e socket.
I can't help much with the OS but what happens if you swap the card to a different PCI-e slot? Does the issue remain? when you uninstalled the drivers did you do a clean install by using the provided AMD program or driver fusion?