iPhone: You have a pretty good selection of apps to choose from if you're looking for an alternative to the iPhone's Music app. If you're looking for something very simple but still packed full of the default app's features, Ecoute is worth a look.
Ecoute's been around for a while, but it has really come into its own recently. Ecoute can do everything the stock Music app can do, but it does it with a great interface that's easy to browse through. You get a great grid-style album picker, albums get their own sections (unlike the stock app where albums are always grouped by artist), AirPlay compatibility, filters for search and more.
Ecoute has a few special tricks too, including podcast integration so you don't need to download a whole separate app, the ability to shuffle albums, Last.fm support, and a night mode so you're not blinded by the all-white interface.
Everything works together with a bunch of great animations, but its still speedy enough that you'll be able to find what you want and start listening right away.
Ecoute 2 ($2.99) [iTunes App Store]