This post has moved to eklausmeier.goip.de/blog/2014/04-01-youtube-video-to-mp3.
Assume you want to download just the music of below video on Youtube, so you can listen to the music on your phone, while you are on the road.
Here are the necessary steps on the command line:
youtube-dl www.youtube.com/watch?v=aHjpOzsQ9YI mv Crystallize\ -\ Lindsey\ Stirling\ \(Dubstep\ Violin\ Original\ Song\)-aHjpOzsQ9YI.mp4 LindseyStirling-Crystallize.mp4 avconv -i LindseyStirling-Crystallize.mp4 LindseyStirling-Crystallize.mp3