You can do something similar with videos, which you can save on your computer as long as you're streaming the video from a website. This means you'll be able, for example, to record any song playing on Spotify or Grooveshark and then save the file on your hard disk in MP3, WMA, M4A or OGG format. The application lets you record any sound coming from a streaming service without quality loss in the output file.
Audials Tunebite Platinum is an app that lets you capture the music playing on your computer on any streaming service, as well as movies from DVDs or other digital content distribution services.