Once fishing in a small Midwestern farm pond, I was bagging giant bluegill left and right. I mean really getting them. But the number of fish on the stringer never seemed to increase. Pulled up the stringer one time and there was a half of a fish on there! Pulled it up the next time and saw the culprit, a giant snapping turtle that was the size of a wash tub.
Several times I've seen trees fall over in the forest. Nothing else going on, no one else around, the trees simply fell over...
One tree to "fall" for no reason was in the forest near Santa Fe, a giant dead aspen less than five feet away from where I was standing (I was recording and photographing historic markings on the tree). The noise was like a cracking
explosion! Scared the hell out of me.
Followed some very fresh deer tracks once in a series of historic gold mine tailing piles. The tracks went off the edge of one pile, and I looked over to see the deer laying dead at the base of an aspen tree. Seems I had 'chased' him over the edge and he hit the tree.
Saw a copperhead snake who was 'fishing' in a small clear pool. His head was above water, and he anchored himself in place with his tail. He was watching a group of fish very closely...
Found a six-foot "chicken snake" in my attic once. Not really an outdoors experience, but given the condition and location of the house, it was very much like camping out.
In Arkansas on the shore of Boggy Creek, home of the Fouk Monster, there was a lot of rustling noise in a swampy area on the other side of the creek. A coyote ran out of the woods, jumped in the creek and swam across towards me. It climbed out of the creek, ran right past me, and kept going! I can only assume the Fouk Monster had frightened it.

FYI, there was a 70s horror movie about the Fouk Monster,
The Legend of Boggy Creek.
In the same area, a rabbit in the woods ran right up to my feet, turned, and ran away. It repeated this several times. I suspect it's den was nearby and was trying to lure me away.
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My strangest night camping ever was a couple of years ago in a New Mexico National Forest. I had set up camp on a hilltop overlooking a ghost town logging camp and cemetery. The area had burned a couple years before and the entire surrounding area was standing dead trees. It was also Elk mating season...
In the night the temperature plummeted and the wind started screaming through the dead trees. Trees started snapping and falling all around, one after the other like a continuous noise, all the while dozens of nearby elk were bugling their heads off. Didn't get much sleep that night... And woke to find the ground covered in snow, and a newly-fallen tree right next to my tent.