An Alan Partridge XBLA game would be ace.
Free-roaming around the city of Norwich, keeping appointments, etc. It'd be like Shenmue.
When you go to meetings or are doing the radio show, it can have a Mass Effect-esque conversation tree. You're presented with three embarrassing options, and using your knowledge of who you are talking to, you have to pick the worst one for that person, in turn gaining Partridge Points.
When sleeping, you can have dreams where Alan goes on a GTA-style rampage against those on the "BBC gravy train".
And finally, you have to be on your toes at all times because a QTE game where you have to press buttons in time to dance can start any time, if Alan daydreams.
Could also have a rhythm-action/Kinect section for when Alan puts on Gary Numan's Music For Chameleons.
All the eurogamers who actually play with each other on xbl rather than just post pseudointellectual pc handwringing bollocks on the forums, love the shit out of biggy.