Yes, last.fm is a free service. You just create a profile and download the associated scrobbler and scrobble your music to your profile. There is a subscription service that offers a few more features but it's in no way necessary to enjoy the basic services.

Last.fm is really easy to use!! All you do is listen to music via Spotify, your mobile device or something that you have connected to last.fm and it will 'Scrobble' your music. This means that it uses the tracks that you listen to, to build up a profile then it suggests music for you.

The music that it suggests is REALLY accurate! Through last.fm, I have discovered LOTS of music that I have really enjoyed and also I have discovered great singers.