From the Last.fm FAQ:
How come I can listen to some tracks in full length a few times, and then they play only as 30 second previews?
If this happens to you, you probably live in the US, UK, or Germany. In these countries, we currently offer a service called Free On-Demand which allows you to listen to specific tracks up to 3 times on demand, in full length and for free.
Afterwards, these tracks will be played as 30 second previous for you. This doesn’t affect the radio – in radio stations, all tracks will always be played in full length, even if you’ve used up your 3 plays limit for Free On-Demand.
How can I get my music on Last.fm?
To get your music on Last.fm, you will need a labels account.
If you already have a Last.fm user account:
If you already have an account on Last.fm as a user, you can register now for an artist or label account.
If you're a first time Last.fm visitor:
You will need to register a labels or artist account from which to manage your music. You can register here. Once done, you will then be able to link up your music to your registered account.
Once you've registered with Last.fm, you will be able to add music to our radio streams, and manage your presence on Last.fm through our Music Manager.
Please note that the Music Manager is currently only available in English.