I had a little dog on a MUP run right under my rear wheel once. Lifted me out of the saddle as I went over him. I don't what made more noise afterwards, the little dog or the screaming oriental lady walking it.
I deal with deer and rabbits on pre-dawn rides all the time. The rabbits are real threats like someone else noted. You really have to watch them darting back and forth in front of the light. I've had deer sight unseen cross in front of me and actually graze my hands on the brake levers. That one had me talking to Jesus. Most scary animal encounter was a great horned owl sitting on a fence post in the middle of the trail. Sucker looked more than 3 feet tall, eyes the size of pie pans in the bike headlight. Didn't see him until the last second, got hit in the face by his wing as he lifted to fly off.
Someone on here has a picture of a rattle snake wrapped up in his derailleur gears and cassette. That is an impressive picture.