My mom got a two-deer-for-one special years ago. We were heading down to Portland to pick up my bro from the airport and hit a doe and yearling. Killed the yearling (I think it hit the tire) and the doe's back was broken so it kept flopping on the road. Called the sheriff dept. but they took over an hour to get here. Fortunately (depending on your view) some rednecks in a pulp truck stopped and put the deer out of its misery with a 2x4. Was kind of surprised they didn't have a rifle with them. Was around hunting season if I recall. Caused about $1500 dmg to the front bumper of my mom's truck, which incidentally the same front bumper had just been fixed a few weeks prior to the deer incident.
Then some idiot came by and wanted the deer meat and asked me to load the bloody carcass in the back of his truck. I was like fuck no bro, you want you load it.
Finally the cop shows up, writes an accident report (needed for insurance claim over $500 dmg), and we leave. Unless you're dead in the road, the Sheriffs or Staties really could care less showing up quickly.
edit: My uncle has hit several deer, one totalled his truck if I recall. I think he even managed to dump his bike when trying to avoid hitting a deer.
Personally I've only hit a bird or two, a squirrel or two, and already dead animals in the middle of the road, that's about it.