Bungee jumping off the Empire State Building.
I'm sorry, but you would never be able to do that. The winds created by such a massive structure causes quite a few things to happen, preventing anyone from being able to bungee jump off of it.
First, there would be a large updraft that would slam you into the side of building. Second, the building sways in huge measures, causing there to be no way of stabilizing the base from which you jump off of. Third, the addition of force on the rope caused by the sway (and air pressure) would most likely cause the rope to break.