The app that has almost always been part of the battle cry from users asking for multitasking on the iPhone has been updated to add compatibility with iOS 4, including the ability to continue playing music in the background.
Version 3.1 of Pandora Radio just hit the App Store a few moments ago. On a compatible device running iOS 4, which is set to be released today, music playing through Pandora will continue playing even when another app is open. Additionally, music playback can be controlled using the remote on the headphones included with the iPhone.
While the Pandora Radio app is universal and will work on both the iPhone and iPad, iOS 4 for the iPad has not yet been released and these new features will not work while running on an iPad.