It would be unbelievably cool to have an application whose job it is to "wrap" an App Store application executable so that it can continue to run in the background (with an appropriate icon or reminder in the status bar). This would be fantastic for apps such as AOL Radio, Pandora, Last.fm, Tuner, SimplifyMedia or Stitcher, so that we could listen to Internet radio in the background while doing other things.
The biggest challenge I see is in preserving the state of the GUI. Does anyone know if this is possible?
Update (2008-10-03): Wow, that was fast! Either someone actually listened to me and developed a Backgrounder within 2-3 days of my post, or else they had a similar idea: