You can record from your video out and audio out using external devices. It could be a camcorder, but instead of recording your monitor, you can try to connect video out of your graphics card to a video in of your camcorder, and line out of your sound card to an audio in of your camcorder.

Instead of camcorder you can use other recording devices including DVD recorders. And you can use capture cards from Hauppage HD PVR (which allows to record 720p videos) to EasyCap (which allows to record SD videos of average quality only, but is very cheap).

Related threads (about gameplay recording, but should work for recording streaming videos as well):
USB 2.0 HD video recorders for recording HD video of gameplays from xbox 360, PS3,...
USB 2.0 SD capture cards for recording SD video of gameplays from xbox 360, PS3,...
USB 3.0 HD capture cards for recording HD video of gameplays from xbox 360, PS3,...