I love Rdio. All the music I want to hear (that happens to be available in their library) for $10 a month. It gets better. I can download the songs to the mobile Rdio apps for offline listening. Even better still, there's an Rdio API and it's pretty rich, as described by Rdio's Ian McKellar in the video below.
The Rdio API allows to developers to be able to do everything you can with the Rdio service, and then some. Its API comes in a few flavors, depending on what you want to do. You have oEmbed for embedding content, REST for grabbing and manipulating data and a playback API for playing back content on the web. There is even an affiliate program, if you're into making some of that sweet, sweet affiliate revenue from your app. You can get paid once for track purchases or ongoing for referring new Rdio subscribers.
All in all, there isn't much you can't do. You have access to user data, collections, playlists, albums, songs, artist data, everything. If you're building an app that does anything with music, the Rdio API absolutely worth checking out.