You can record games played on your PC with Fraps.
If you want to record from a console, then you'll need to invest in a capture card. There's Dazzle, cheap but not that great quality. For HD quality, you could use the HD PVR. Personally, I use a Elgato.. I think they are cheaper than the PVR, but I don't know.
Here are some links:
Fraps
HD PVR
Elgato
Dazzle