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.