Audacity will let you select from the available sound sources. If your sound card (or the onboard sound from your motherboard) supports it, you should be able to change the source so that you can record whatever your PC is playing:
http://audacity.sourc...recording&i=streaming
However not all sound cards (or motherboards) can interact with Audacity (or with any similar program). Under those circumstances you need to use a 'jack-to-jack' lead to connect the sound output from your PC to the sound input (and then select 'Line In' as the source for your recording.
Alternatively, there are loads of online services which claim to be able to produce an MP3 file from a Youtube video, such as this one:
http://www.youtube-mp3.org/
(I've not tried that one. If it's no good, simply google 'youtube mp3').
Or you can use a free program specially designed for the task, such as this one:
http://download.cnet....5553.html?tag=mncol;2
Chris