I have two answers for this question, depending on what do you want specifically, there are many to choose from.
1. If you are just looking for an app to play the music you have (synced) in your iDevice: try track 8, audyssey media player, audio player 7.1, CarTunes music player, headquake and the list goes on. I like track 8 but I always go back to stock player.
2. If you are looking for a whole different category like streaming music services, radio-like or on-demand the competition is tough.
Radio-like: pandora, slacker, groove shark, iTunes Radio, songza, google play music (free) etc.
On-demand: Beats music app, Spotify, Rdio, deezer, google play music all access (paid service) etc.