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This is my entry for the extend the function competition. This could be huge...if only a major game publisher will pick it up. Basically it turns your iphone into a 4 input joystick. Use two thumbs and both index fingers to squeeze to the screen the extended, flexible arcs that when filled with conductive material they will effectively transmit capacitive input on the screen. Only works in landscape mode and will probably block a few mm of view.
This is the conductive counterpart which should be printed twice: http://shpws.me/whcn
Of course Apple explicitly states that no metal should touch the screen, but this is the only conductive material shapeways produce.
This is of course not the only use of the case as it's obviously extending the aesthetics of the phone.