Cycloramic rotates your iPhone 5 automatically while shooting video (completely handsfree) then it stitches individual frames from the video together to compose a seamless 360-degree panoramic photo. There's a tutorial video of it in action here.
Cycloramic is one of those rare apps that turns up every once in a (long) while that's almost indistinguishable from magic. (Remember Word Lens from 2010?) When I first heard about it I was sure that it was a hoax.
As with every cutting-edge (ahead of its time?) app, it also comes with a healthy dose of caveats. For starters, it only works with the iPhone 5, and it only works on glass, marble or shiny surfaces. You also need to set your iPhone to 'Vibrate on Silent' and 'Vibrate on Ring' (Settings > Sounds > Vibrate on Ring > On and Vibrate on Silent > On) or it won't rotate.
Cycloramic currently records video only, not sound (presumably because it would capture the sound of the phone vibrating against the surface). The developer, Egos Ventures 2012, promises to release an update "soon" that will be compatible with iPhone 4/4S.