I had some problems like that in the past. Over time I had to replace my power supply, my motherboard and my video card. Was nuts. All were good name brands too (Antec, DFI and XFX).

It's very frustrating trying to narrow down the problem. Does it happen when you use Office apps or surf the web? or games only? WoW only?

It really sounds like a hardware problem though, but it's often hard to diagnose. Typically I just buy a new PC :P and eventually fix my old one. I have too many computers under my desk atm. They all run wow fine though!!