I absolutely love Grooveshark, and kicks Spotify Free out of the water.
Search for music by any artist you wish, and 9 out of 10 times, you will find it. The quality is very good however since the users upload the content, some can be of poor quality or mislabeled.
You do not have to sign up and there are no adverts like Spotify either so since your song finishes, it will either play the next in line, or find a new song and play it.
There is an optional mothly fee without any adverts, but these are only visual and can quite happily live with them. It is waste of money, but for $5 a month, if it bothers you it will be worth the cash.
Overall, its a good alternative to Spotify who have lost their way, the quality is good and there is a good selection, and there are no adverts! What are you waiting for? Go to Grooveshark and play to your hearts content!