How can I record what's on my computer screen?

I need to make a portfolio of game levels I’ve designed, so I’d like to be able to play through a few minutes of a level, and have the gameplay saved to an .avi or .mpeg or quicktime file or something. Is there an application that will do this that won’t cost an arm and a leg? Ideally I’d like the output to be a file format that can be edited, although I’m not sure I can afford that either. Is there some sort of shareware or stripped down version of Premiere available?