This is an old thread, and my reply below is no longer true. To sign up without Facebook, go to the sign up page and click "create an account using your email address"! If you signed up using a Facebook account, you must make a new account to be separate from Facebook.
original reply below, no longer true:
An active Facebook account is required to use Spotify.
If you registered before September 22nd 2011, just log in with the username you created during the registration process. If you signed up after then, you are tied to Facebook and can't use Spotify without it.
You can give kudos points to this "Idea" if you hate forced Facebook: http://community.spotify.com/t5/Spotify-Ideas/No-more-facebook/idi-p/33811
You can also give a comment that Spotify employees will ignore like they always do when it comes to forcing people on Facebook. Nothing has been done for 7 months, so I'm afraid this is going to be a permanent change. No Facebook, no Spotify.
I chose my username because of this, by the way.