Major League Combat is a sport that combines juggling, rugby, Capture the Flag, and maybe Quidditch? I can't make out how you score, but keeping your juggle from end-to-end seems important.
Weird sport or the weirdest sport? It's definitely up there with chessboxing. (thx, benjamin)
Juggler Scot Nery lists eight reasons why you, as a normal person, should learn how to juggle.
Sometimes it feels like A.D.D. makes you better at stuff, but when it comes down to it, we really need to be able to sit still and focus until something's done. Juggling builds your focus muscles through regular practice and a built-in rewards system.
Here's how to get started.