Last week I played around with Spotify Web API and made something really simple: Music Explorer. Just type any artist, album, or songs in the search box and it will display relevant results depending on the query. When you click on each tile it will play a 30-second preview of related song. You can also click the 'Play on Spotify' button and it will launch the Spotify web player on a new window.
Live demo: http://umisyam.us/playground/explorespotify/