I personally don't.
I had a buddy last season where a back-brace. He loved it and it saved him from some pretty nasty falls.
Compression shorts are worthless and usually cost a lot of money. They don't protect your tail bone very well - typically just thighs.
I know some people wear mouth guards and absolutely swear by them. I'm gonna spend more time this season going ham sauce on rails so I might pick one up when I try new things. I don't want no missing teeth from biting on a handrail
I know you can also get gloves with built in wrist braces to protect your wrist from breaking on impact. I would typically say that's meant more for snowboarders only because of the way they fall (forward or backward and break falls with arms).