Originally Posted by Kentucky
A cutting, team penning, or reined cowhorse would be easy choices, but so is mounted cowboy shooting.
Jousting (true jousting when done with intent and correct tack and weopons) would be something I would watch, as well as mounted archery.
Polocross is also on the list.
Ok, I listed six events, i've only seen cutting in person.
Aw, that's a shame ): you should see the full contact jousting done by the Knights of Avalon and the Knights of Mayhem or the Sonora Jousting Championship. It's all real lances, real blows, real falls. None of the 'medieval times' crap with the half lance and the slow speed and the over-acted everything.