LifeDriver

I use a free piece of software that will do this and runs on Windows and Linux (It runs on Mac but for the time being won't make record streaming audio):

Audacity

Ogg should work right away, but to make mp3s you will need to grab the LAME decoder. Instructions for this are found here:

Installing LAME in Audacity

Once you have everything, look here to see how to do it:

Recording Streaming Audio with Audacity

For Mac stream recording they recommend Audio Hijack or Wiretap Pro.