How can I extract the audio from a video file?

I have a video of a music performance that I downloaded online, and want to extract the audio so that I can store it as a music file. It's a MOV file with the Codecs - "XVID, MPEG Layer 3." What software should I use for best results?

I can't tell you about best results, but for some results:

VLC, FFMPEG, or MPLAYER

VLC has a GUI and a Wizard. ffmpeg and mplayer example here.

If it is a MOV file which you can open with QuickTime Player, open it QuickTime Player 7, an optional install in Snow Leopard, and then go to File -> Export, and choose Sound to AIFF for instance. The resulting AIFF file can me converted back to MP3 or AAC with iTunes, for instance.