One year I tagged 1 deer and had 3 deers tagged me...the most damage my car ever took was a broken door lock and some paint scratches. Very lucky indeed. I had a friend who was driving one night with his passenger window down. A deer jumped through the window while he was driving down the road. He was trying to steer the car and fight off the attacking deer. He ended up in pretty rough shape....broken nose, bruises, and alot of cuts. His auto insurance company ended up balking on the medical bills because he didn't actually hit the deer so it wasn't deemed as an automobile accident.
In Missouri you're usually allowed to keep whatever you hit.