The Nile River here has a Bungee jump. I haven't been brave enough to experience it, but my kids have and so have some of our visitors. Diving head first into the river to have your shirt yanked off over your head as you come up isn't quite my idea of fun.
You can always shoot the class 5+ rapids in a kayak or in a raft if bungee jumping isn't quite your cup of tea. The locals like to strap on jerry cans and shoot the rapids that way. What ever "floats your boat" I guess.