In my previous post, I talked about downloading videos from various video streaming sites including Youtube. Here's one way to download mp3 from Youtube videos. Like I said, you can prefix your Youtube URL with the word 'kick'. It takes you to a site where you'll have a lot of formats to download from. One of the formats is mp3. So you can download the mp3 of your favourite video.
There's another way to do this. Go to ListenToYoutube and paste the Youtube URL and the site converts the youtube video into corresponding mp3 and gives you the link.