My specs are:

AMD FX 6100 3.3 GHz
OS: Win 7
Video Card: AMD RAdeon HD 6570
Open GL: 6.14.10.11931

Blender simply crashes whenever I try GPU rendering. Any suggestions are appreciated.

You might try running blender from the command line to get interesting messages.

I suspect the problem is some combination of AMD video card + CUDA support + video memory.