Ultimately there are a few problems with apps like this, not the least of which involves a lack of payment to the artist*. Through the magic of YouTube, however, I found a couple of solutions that won't cost you anything (except maybe your soul), and allow you to make playlists. Everyone is trying to make money in the music game, so to get the most out of these services you'll wind up needing a subscription. I've also been a big fan of Slacker (the comedy channels are awesome), Stitcher (for news) and TuneIn (for local radio stations). I previously subscribed to Spotify, Rdio and Pandora.
Engadget has a good writeup of the Beats Music experience here.
Today Beats launched its own music service, which I'm trying out for the 7-day trial period.