I first discovered Rdio in 2011. Streaming music was a new idea at the time and not a lot of people were willing to pay for a subscription to listen to music they didn't own. Three years later, things are a bit different and a lot of people exclusively listen to music streaming through Pandora or Spotify.
I prefer Rdio because of their focus on music discovery. The service makes it easy to find new music based on your musical tastes. Rdio is now offering a free tier to their listening options. In my opinion, it is the best option for streaming music. Check it out at rdio.com.