OK, that's helpful.
Make sure you have all current updates applied (Go to the Apple menu in the top-left of your screen and choose "Software Update...").
If that doesn't help, you might need to try and re-install iMovie?
Have you installed anything recently that is related to video playback in any way? Any plug ins? Any apps like Flip4Mac or Perian? Any sort of Divx player or anything?
Is Quicktime working OK? Try and open any video file with Quicktime and see if it plays there OK.