Despite my threads title, I really wasn't that interested in jumping off or swinging on an arche as much as I am in just rappelling from one.
You can still rappel off Corona; in fact, the standard way to descend after doing the climb up there is to rappel.
See my November 28 trip log entry:
http://www.summitpost.org/2014-trip-log/884198
People should be extremely careful not to damage the arch though.
You can also climb Looking Glass Rock:
http://www.summitpost.org/looking-glass-rock/197860
It's a popular climb. The way the anchor station is set up, you can't really damage the arch. You squeeze through a hole and step off the rappel and it is immediately free hanging and little or no rope drags across the rock.
You actually rappel right through a smaller arch that is right next to a gigantic one. Only the smaller one can be seen in this photo of me rappelling through. The huge one is just to the left:
This is the view of the huge arch from the top of the rappel (though it's hard to tell from the photo just how big it is!):
Morning Glory Bridge (right outside Moab) is part of a popular canyoneering route known as Medieval Chamber:
http://www.summitpost.org/morning-glory ... ber/394414
People do rappel off the arch, but since there is no anchor you have to do a simul-rappel with one person going down each side of the arch. It can be very dangerous if you don't know what you're doing and it would be possible to damage the arch if you didn't use pads. I think it's much better just to rappel through the gap between the arch and the rock wall. After walking across the arch, you can rappel the rock wall, which is safer and it doesn't have any risk of damaging the arch. It's still a really neat rappel:
Of course for any of these methods and routes, they have to be done correctly, for safety's sake.