In the immortal words of a great (if animated) American, Home Simpson, D'oh. The Spotify application has reportedly gone back to invite only status.
The app only recently hit the Android market, and if you didn't grab it whiel you could you may be too late. The app has reportedly gone back to invite only status because the company couldn't handle the glut of new registrations.
This is not such a surprise, Spotify had said before that if too many people signed up it would go back to invite only. If you really want Spotify, you can still sign up for a premium account only the free ones are via invites only. The service currently has about a million users.