No need to buy expensive software or hustle around with command line freeware.
- get and install VLC media player
- copy URL of desired youtube video
- open VLC
- Media|Convert/Save|Network
- enter URL
- press Button “Convert / Save”
- enter Destination file. IMPORTANT: Should end with “.avi”
- Chose profile “Video – DIV3 + MP3 (ASF)”
- Press Button “Start” and wait
- 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.