Oh boy I have a few.
Was doing a huge laurel oak removal. It was decayed and declining heavily. I pieced out a 10' section or so, and as it hit the ground a racoon came rolling out. His mate followed suit out of the remaining spar from about 30' in the air. The thud could be heard with the chipper on.
I was pruning at a heritage site one day. As I was climbing around I heard some squealing. I tried to find the source but could not. There was a large dead limb that needed removed. I commenced with it's removal, and evicted a flying squirrel nest. I felt terrible. We put the nest back in the tree with the hope that momma squirrel would come back and take care of them.
Was on a last minute job in Ohio when I was fairly green. I was tasked with pruning some mid sized tree, only requiring a pole saw. I start poking around to decide what to cut, and poked a possum in the butt. He shot out of the tree, turned and burned between my legs. One of the fellas I was working with screamed, he was scared of possoms.
In Florida, the palms are infested with rats and critters, including iguanas. I was working with some cuban men pole pruning these palms on a deck. I let a frond rip, and a massive thud from a 30lb iquana shot over the jobsite. One of the guys, without a beat, shot off after him, between the deck slats and out to a river. I guess his family eats them.
A buddy almost got bit by a rattle snake. He leapt out of an apple and landed all but 3 feet from it. Took off running like a bat outta hell. We came back and he got vengance by taking its head.
I'm sure there's more, but I'm tired and can't think of any.