Yup, almost had a rabbit related off once.
Flying down the lanes on the road bike, passing a farm on the right hand side, when all of a sudden a rabbit comes flying out of the yard, and right under my wheel. What the... Didn't see it until I was right on top of it, how the hell I stayed upright I do not know. I look around as quick as I can to make sure I'm not seeing things, or whether the bike is damaged in anyway. Said rabbit is fine and making a dash for the hedge, now hotly pursued by the farm Jack Russel, which now is heading for my back wheel. I somehow miss the little sod, who is oblivious to me, and I carry on, wondering what just happened.
Lucky day I guess.