It should be possible with most recent sound cards. Select Mixer input for your sound card and then use the software of choice to record the streamed audio. Unfortunately, when you capture sound in such ways, the sound that is streamed is usually sampled at lower rates, but your sound card records at higher rates. So, you get ineffecient copies of the streamed audio, but it still works.
Although I don't know of any programs which can capture streamed audio to files without re-recording the audio, it may be possible to find them somewhere.