How can I record video from my webcam?

One way is to use FFmpeg with the following command line:

ffmpeg -vd /dev/video0 -an -vcodec mpeg4 -s 640x480 output.avi

This records video (no audio) from the /dev/video0 device at a resolution of 640x480 and writes it to output.avi.

Thanks to Vidar Normann for this tip.