A new tool called iPhone Backgrounder is now available for jailbroken phones which allows you to run official App Store apps in the background. The timely release comes just as Apple's missed the September deadline for background push notifications.
Backgrounder is a Mobile Substrate-based extension to Apple's SpringBoard application launcher that allows applications to run in the background (applications are normally terminated upon suspension).
To enable backgrounding for the app you are currently running, you simply press and hold the home button until a message pops up telling you that "Backgrounding Enabled".
Users can also set up an XML file that will enable backgrounding on specific applications by default. Detailed instructions are provided. Users must have a jailbroken iPhone to take advantage of this application.
Apple has restricted the use of background applications due to concerns about memory and battery life, so your experience could vary.