Audacity works well - I use it a lot to record radio shows, then burn then and listen to them in the car (at a more convenient time for me )
The best bit is that Audacity is free

http://audacity.sourceforge.net/

Easy to use too - start the streamed audio with Audacity open after you have clicked the red record button - you will see if you have input as there will be a wave form.
As BK says, just make sure you have the input selected properly - if you have a microphone make sure it is not operating, as it is possible to record the audio, and background noises at the same time

When you have the wave form, you can export as a wav, and edit to give MP3 etc as needed. You can also edit to remove commercials / blank noise etc, and remove background noise fingerprints etc if needed.

You just need quite a lot of memory because it record as a wav file.