Mountain unicycling is very awesome. Mountain unicycling, nicknamed MUni, is about maneuvering the unicycle down rough terrain, Preferably steep terrain with lots of loose rocks and drops. You have to stay concentrated on the trail in front of you, other wise, you will probably fall. A fall like that is called a idiot fall, well that's just what me and my friends call it. Its really referred to as a UPD or UnPlanned Dismount. When Mountain unicycling, I wear lots of protective safety gear, including wrist guards, knee/shin guards, a helmet, and anti gravity boots*. I can't tell you how many knee's I would have lost by now, had I not been wearing my trusty knee/shin guards. Well actually, I guess I probably would have lost just two knees by now, having only two knees to lose. Well, unless I lost both knees at once, I would probably just lose one knee and not be able to unicycle for a while.
You really have to navigate the unicycle around or over every bump. You cant coast over things like on a bike, you have to pedal the whole time. Alot of the time you can use your momentum to keep yourself going, and if you get going to fast, you fly forwards and die**.

Trials unicycling is also, very awesome. You can do trials almost anywhere. Trials is basically jumping around, on to, across, and over things, on your unicycle. Watch some videos of Kris Holm talk about trials. http://lutkus.com/video/Kris_Holm_workshop/

Freestyle is like figure skating on a unicycle. There is Pairs freestyle, with two people doing some sort of coordinated routine. And then there's women's freestyle, and mens free style, and all different age groups, oh man, lots of freestyle. When you watch freestyle, you don't expect much, but then a tiny girl stands up on the seat of her unicycle and does back flips***. Well, something like that, its pretty amazing.

Unicycle racing is just what it sounds like. There are lots of crazy events where people go way faster then you expect. Here is a link to the official site about unicycle racing: http://www.unicycling.org/usa/competition/racing.html It will tell you more then I will ever be willing to type.

*there is a good chance I am lying.

** yup, I am lying

***100% true. not lying at all.****

**** I may have lied.