Computer crashes when playing games?

When I begin playing a game, it runs perfectly smoothly, even on high graphics settings. After a 1-5 minutes however, my PC will make this sort of revving noise, followed by the fps getting choppy, if the game is not immediately exited out of, the image crashes and the sound that was playing loops, creating a buzzing sound usually. I have tried this with a number of games, all wielding the same result in the end.

Games tested with: World of Warcraft, Minecraft, Orcs Must Die and Skyrim. I can play less CPU intensive games such as Minecraft for longer than, say, Skyrim. I have cleaned out my tower with compressed air, de-fragged and error checked my drive, all with no result.

This is really bugging me as I'mm unable to play any of these games I've purchased, this problem has persisted for about a week now and I'm tired of it.

Crashes are sometimes a way for a computer to just throw their arms up in the air and scream "I can't do this". Your most likely crashing because you don't have nearly enough RAM to run the games along with the necessary programs, drivers etc. Necessary for windows to run. Thats like trying to drive cross country on a gallon of gas. Check the game requirements, check and see how much available RAM you have and do the math. Add RAM, upgrade video card, etc.