Why does my computer crash when i play most games?

I'm using a Windows 7 Home Premium, 2 year old desktop, Pentium dual core CPU, 2.6o GHz, 4 gigs of ram, 64 bit machine. I have 5 users on this computer (not my decision), and 144 gigs of space left. I can play a few FPS' like Combat Arms (bleh) and A.V.A. easily enough. But other games like Fallout: new vegas and Grand Fantasia And perfect world give me trouble. i can start them up fine, but after ten or twenty minutes my computer says "entering power save mode" and shuts down. i have to manually turn it back on. Does anyone know why this happens?