iPhone-Backgrounder (available for jailbroken iPhones via Cydia) brings another much-desired functionality that Apple's not allowing for legit apps—the ability to run in the background. After installing the extension, simply hold down the home button on the app you want to preserve, and it will keep running until you tell it to stop with another home button press. Looks like those jailbreak folks aren't done innovating just yet...
Like copy and paste, the only way to bring system-level functions to the iPhone remains via jailbroken software. If you have the "BigBoss & Planet-iPhones" source loaded, iPhone-Backgrounder should show up as a default install option. Our tipster says he's got Pandora playing while receiving background IMs while syncing at the same time (crazy!). He reports some bugginess with duped IMs and the like, but on the whole it's working as expected. [iPhone-Backgrounder - Thanks Horn!]