I'm a big fan of Google Music, or Play Music as they call it now. I like the UI, and I like that everything is in cloud. You can also make specific songs/playlists/artists/etc available for offline use if you need to
I've been using the simple "android music" app. If you're looking for something simple that's the one to go with! I've been browsing around because I'm not fond of play music and Motorola's music player is a pain in the butt so I found this one.