I have had this same problem with a brand new Radeon HD 7770. I have done much research on the matter, and heard various responses and feedback regarding what is supposed to be the problem.
After much trial and error, I have finally found a confirmed solution.
It is NOT a RAM issue, it is NOT a motherboard compatability issue, it CAN be related to a PSU issue (I will elaborate below), and it is NOT an outdated driver issue. Direct X is also related.
Games that it crashed for me randomly every 5-15 minutes:
Starcraft 2
Tribes Ascend
Games that it did not crash, League of Legends.
It is suggested that it does not crash in LoL because that uses Direct X 9.0. Any game that uses Direct X 10, or 11, are the ones that crash.
To fix the problem follow these two steps:
Go into Power Settings - Set all values to "NEVER"
"Put computer to sleep - NEVER" "Turn off display - NEVER"
Step 2:
Open up your GPU's manufacturers software (and/or use a program such as MSI afterburner).
Go into the overclocking settings - Reduce Core Clock Speed by 150. (so for example, my 7770 has a 1150 default core clock speed. I reduced it to 1000.)
I have followed both these steps, and have not crashed since. Hope it helps!