Apple had pulled out Push Notification Service; their solution for one of the features that we have been asking for, the ability for iPhone apps to run in the background from the 4th beta version of iPhone firmware 2.1 for "further development".
So till Apple does not introduce the feature, you can use the hack developed by Gaizin for jailbroken iPhones, called iPhone Backgrounder, which allows users to run iPhone apps in the background.