At monument valley, there used to be a herd of goats that would move across the runway in the morning, and come back eastbound in the late afternoon. A small dog moved them. Where they came from, and where they went, I have no idea. But they were as regular as clockwork.
Indians on the runway at San Carlos; they'd jog there in the morning, and seemed to not notice us unless we did a low approach and "forced" them off the runway.
I had to chase a bull off the runway at Shiprock once, with a .45 auto. It was close to dusk, and there weren't any lights. By the time we got the bull far enough off the runway, it was nearly dark. We parked an ambulance at the far end of the runway with it's lights shining toward us, and took off toward those. It marked the end of the runway, and if the bull tried to reenter the runway, we'd see the silouette. For safety, approaching the point adjacent to the bull, I dropped flaps, climbed to bull clearance altitude, and then dropped back down on to the runway on the other side, before accelerating to finish the takeoff.
I've had to go around for skunks, deer, antelope, and folks who suddenly materialized riding horses on the runway. Coyotes usually just sit there; they don't seem to get too excited about takeoffs and landings. I had a large tortoise on the runway in Florida once; I watched him suck up inside is shell when we powered up. I imagine he moved clear after we left, because there weren't any big stains on the threshold when we came back.
I've had probably several thousand bird strikes. Most of them little ones, but sometimes when working a field we'd hit what I used to call a flock of popcorn birds. They'd lay down in the crop where they apparently couldn't hear us coming. When we were almost on top of them, they'd come flying out of the crop all at once, and the sound of them striking the airplane was a lot like popcorn. Occasionally they'd wind up in the cockpit; the worst ones made it past the prop, rode the blade wire cutter up the front of the windscreen to the cockpit ram air intake, then exploded into the cockpit and down the back of my shirt or flight suit.
I had a large falcon strike the leading edge of a Cessna 210 once, and peel it back to the spar. I've come back lots of times with birds lodged in the airplane, inside flagmen, gear wells, intakes, all over the place. Sometimes the whole bird, sometimes just part. I hit what I believe was a really big owl on halloween one year, late at night (or early in the morning, depending on how you look at it). Not enough left to tell, but a lot of blood.
I've had birds make it past the windscreen and into the cockpit a few times. Lots of insects; wasps a fewtimes, a bumblebee or two. A mouse. Several birds that got into the airplane and spent their time flying back and forth. Two large bull snakes once, but we never got of the ground with them. I wanted to save them, and the boss killed them. I've never seen a 70 year old man move that fast, and wouldn't have guessed he could be so vicious.
Several ducks that came away in surprisingly good condition; they probably could have been mounted. Lots of insects, of course. Everybody is used to smashing bugs, but you haven't seen smashed bugs until doing low level runs on an insect infestation such as greenbugs or russian wheat aphid for hours on end. You can wipe them from the wing leading edge like a thick paste. It's disgusting.
I've cooked a few birds that were nest building in the engine compartment and didn't make their presence known, and a few that have attempted to fly out after the prop is turning.
I've had a few close ones with antelope during the takeoff roll. I didn't believe that they went under fences instead of over them, until I saw one go scooting by during the takeoff. It didn't break stride as it approached the fence; went down on it's knees, or whatever you call an antelopes knees,and slid under the fence, went right back up on the other side and kept going. You get used to them after a while, but they're still goofy-looking.
Several company airplanes hit horses over the years on the Navajo reservation. I had run-ins with dog packs on the runway several times at Chinle (old airport). Carriage of a firearm was a really good idea there after dark. Horses on the runway weren't uncommon. I landed one night to find an airplane sunk up to it's axles in the runway; it fell through the frozen top layer.
It wasn't animals, but I watched one of our airplanes go through a set of train tracks, a cedar post fence, a 1/2 section of corn, two other fences five times, and a billboard, before striking a tree on the edge of town. That was fairly dramatic, and I'd have bet anything it wouldn't have made it through the fence that many times. Does the tree count?