Every Android phone comes with some kind of music player software. While each one has its own perks, Double Twist takes the best of them all and has it work on most Android devices (Android OS 1.6 and up).
I have been using Double Twist for a while now, and I'm for the most part a fan of the complete stock experience. Double Twist adds great features like sync support (optional wireless sync add-on in the market for $4.99), lock screen controls and a nicer interface to name just a few. It syncs when hooked up to your PC or Mac with their free software, and can pull playlists and music from other popular desktop software like Windows Media Player and iTunes.
Our friends over at Tech Crunch noticed that the Market page for them shows that they now have over 1 million downloads. You can get the app FREE from the Android Market here, and you can upgrade it to support wireless synching with their add-on called Air Sync for $4.99 also in the Market here.