What risks do mma fighters put on the line medically when fighting? I am a huge fan but I was curious so I thought i'd ask.

There life. They injure any part of there body or damaged it.
Too many to list. As a ring doc for professional mma events (strikeforce, kotc, ufc) I am always seeing "new" injuries. There are the usual cuts, concussions, etc, but on the last ufc event in seattle a fighter injured the inside of his mouth! It is a very dangerous sport. Any part of the face can be damaged, any joint, any bone or tendon can be injured. Basically they put it all on the line.
Some common ones. I train in mixed martial arts and I'm also a ringside physician, having doctored UFC, Strikeforce, and numerous local events. The most common injuries I treat are lacerations. Also very common are contusions and sprains. Anytime there's a loss of consciousness, I'm concerned about a concussion, no matter how brief the fighter was "out". Those are the most common injuries, but anything can happen.
MMA injuries. Buse gj. No holds barred sport fighting: a 10 year review of mixed martial arts competition. Br j sports med. 2006;40 (2):169-72. Ngai km, levy f, hsu eb. Injury trends in sanctioned mixed martial arts competition: a 5-year review from 2002 to 2007. Br j sports med. 2008;42 (8):686-9.