Why does my computer shut down randomly? Most often happens while video-chatting on Skype.?

It just blacks out and that's it. No closing of programs to do a nice shut-down. It's like the power for the whole system goes out. It mostly happens while I'm video-chatting on Skype. Only once has it blacked out while not on Skype. My computer also has blue-screened a lot and I'm not sure why. Always says something like: memory error. Whenever I reset my network adapter, sometimes my computer will blue-screen.