I think it was/is Audioscrobbler, or at least that is the plugin you can install on your PC to track the music you listen to. Now last.fm has deals with three of the major record labels so if you join you can listen to artists on those labels for free (albums streamable three times), and there are many other labels such as
Mute,
Tigertrap,
Revive and
Labrador (some cracking Swedish indie-pop) who put their bands content up for free streaming too, as well as many unsigned bands like The Cakes...
There are also playlists, and 'recommendations' radio, and more...I've found many great bands through last.fm. :)