Downloading from YouTube is increasingly getting popular and there are lots of programs that are able to do this, some of which costing quite a bit of money.
One I think is good is Vixy, which is a web site that is quick, free, and easy to use. Just paste in the Youtube URL and select an output format, and within a minute or so the site will fetch the video, convert it to your desired format, and allow you start downloading. One of the formats is MP3 audio, so if there's a music video on Youtube that you want to listen to on your MP3 player, now you can.
Vixy link