No need to buy expensive software or hustle around with command line freeware.

1. get and install VLC media player
2. copy URL of desired youtube video
3. open VLC
4. Media|Convert/Save|Network
5. enter URL
6. press Button „Convert / Save“
7. enter Destination file. IMPORTANT: Should end with „.avi“
8. Chose profile „Video – DIV3 + MP3 (ASF)“
9. Press Button „Start“ and wait
10. Done

Of course you can chose or create any other profile you like. Or use a raw file output to edit files with virtualdub.

If you only want to keep the audio track chose an only audio profile.