This hack available on jailbroken iPhones allows you to hold down the home button when you quit an app to have it continue running in the background. Considering this is homebrew software, it’s probably trivial for Apple to reproduce it but, as we all know, Apple does what Apple wants to do.
You can even add some XML code to assign apps that run in the background by default, a handy little trick for keeping IM apps in the background. Apparently there are still some bugs but this is an impressive little bit of innovation from the homebrew community. Who said Pwning was dead?
You can download the app through Cydia, the iPhone homebrew installer.