Growing up in the Appalachian mountains in Pennsylvania, I encountered Pennsylvania black bears fairly frequently when hiking or fishing. Only once was there any altercation when a couple of cubs decided we hikers looked fun to play with. We hikers took off running downhill just as fast as we could and kept doing it until we reached a creek swollen with snow melt. We plunged into that stream and quickly decided we'd rather face the bears. Two or three steps and our feet and legs were frozen! Fortunately, the cubs had given up their interest in us and Mama's only interest (as ours) was keeping us away from her cubs. Pennsylvania black bears eat mostly berries and grubs. They tend not to be aggressive and there's little cause for fear.
Hunters swear that they see mountain lion/puma/cougar in Pennsylvania and Virginia woods, though our departments of environment say there aren't any. I suppose the trail cameras must be lying, as certainly the government agencies must know best. I have seen bobcats, which are a smaller wild cat. I've even had one that used to come quite often to yell at a racoon that lived in a maple tree outside my bedroom window. I don't know what that racoon ever did to the bobcat, but that bobcat surely gave the racoon a piece of his mind with monotonous regularity. I'm not sure if you've ever heard a bobcat scream, but it sounds like what I'd imagine a young woman would scream like if one were to pull her legs off. It's an absolutely horrifying sound, extremely loud, and the bobcat was literally five or six feet away from my bedroom window. There was no sleeping until the racoon was sufficiently chastened.
Timber rattlesnakes are more of a problem in Pennsylvania and Virginia. They tend to inhabit the big piles of leaves that collect at the bottom of cliffs alongside the better trout streams. They are the primary reason that I took to wearing waders moreso than protection from the water, as trout streams make for cool and pleasant wading in the summer.
I did have a small grizzly bear wait his turn for my fishing hole in Alaska once. My fishing partner and I were swapping fishing pools bank fishing alongside a river in western Alaska. I had just leapfrogged my partner and started to fish a nice pool where I was taking some good rainbow trout who were gorging themselves on salmon eggs. The king salmon were spawning, and so were protected from fishermen at that moment. A shame as the king salmon were enormous. We contented ourselves catching large rainbow trout. My partner's pool stopped being productive, so he walked past me to the next pool. When he got there and looked back upstream to me as a regular safety check (always know where your fishing partner is when in back-country), he said very casually, "Oh hey. There's a bear." Our guide looked over to see a grizzly sitting on the beach watching me cast to the trout. It seemed patient, but we nevertheless got in the boat and went to midstream to watch what the bear would do. Once we had left, he waited a little while, then went into the river right into the hole I had been fishing. The king salmon were not protected from grizzlies (as if there were protection from grizzlies in any situation), and it proceeded to grab and eat four or five large salmon as daintily as a socialite nibbling on shrimp at a cocktail party. I, for one, was grateful that the bear's mother had taught him manners and patience. It was a fairly small grizzly. The guide guessed that this was its first year away from its mother (which would make it three years old, I believe).
We also saw an enormous grizzly walking the opposite bank of a different river we were fishing. It crossed the river well up from us and walked up a tributary to do his fishing. We later walked up the tributary to check out his foot prints and they were at least 10" across.
The socialite grizzly.
We were also chased off the lake shore by a moose. It is little known, but moose kill more people in Alaska annually than do grizzly. They are very territorial, absolutely enormous, and entirely unstoppable once having set its mind on an objective (such as disemboweling flyfishermen). We left everything - tackle, lunch, spare gas, etc. - on shore, got in the boat as quickly as we could, and shoved off. Fortunately, this particular beach had a very steep drop off. Only a few feet from shore the water was well ever 10' deep. Fortunately, I had not yet moved my camera out of the boat, so I was able to get some photos.
I was also attacked by a tern to whose nest I must have walked too near.
100's of these were caught. All fish but for one pink salmon that was unfortunately hooked too deeply to release safely were released. The pink salmon was eaten for lunch.
My best rainbow ever - 23" long.