If you want to be on Spotify, you're going to need to be on Facebook too. Go to Spotify now and you'll see this message: "You need a Facebook account to register for Spotify. If you have an account, just log in below to register. If you don't have a Facebook account, get one by clicking the 'create an account' link below."
A big feature on Spotify is seeing the playlists of your Facebook friends and letting them see yours. Everyone discovers new music and it's like having your friend make you a mixed tape but without the effort or the tape. Of course, some people would rather just listen to music and not join Facebook at all. Tough. Spotify says it just wants to make registration and sharing easier and the best way to do that is to use Facebook.