Hi Geirs- Are you trying to stream music offline or via your mobile? If so you will need a Premium subscription.
An Unlimited subscription allows you to listen to music with any adverts or limits to the number of hours you can listen to. Premium allows you to listen playlists offline on your desktop/ mobile device.
This page of our website provides a great summary of each subscription if you want to compare your options: http://www.spotify.com/get-spotify/overview/