Update 2010-Nov-11: Apple has come out with AVQueuePlayer in iOS 4.1, and presumably most people are going to move to the latest version now that it performs well even on the 3G, but the AVPlayer can still be used to manually create a queuing of items, but if you want all the hard work to be done for you, with only a few limitations, then use AVQueuePlayer instead.
Update 2010-Oct-19: Apple has been updating their documentation slightly, and it has more information now with regard to setting up an asset. This is more specifically for video, but it might help fill in the blanks for just audio. AVPlayer Playback Guide
The iOS 4.0 framework introduced AVPlayer which allows playing a MP3s from the iTunes Music Library in the background without using the iPod music player. This has a couple benefits over the MPMusicPlayerController in that you can add new items, stop, or play music in the background. Also, a custom icon can represent your app in the multitasking menu where the ipod controls are located. If you stick with [MPMusicPlayerController iPodMusicPlayer] you can play music in the background through the ipod player, but once an app goes into the background, it no longer has control over the playback of the music.