I've not yet actually been hunting (make all the newb comments you want) But I have done a ton of backpacking and seen some strange things.
I was walking along a raised jeep trail through a grassy marsh down in Myakka River State Park, to my right was a small pond to my left was a wide open marsh where hundreds of egrets, herons, and sandhill cranes were wading and feeding. As Im walking along a doe was staying about 15 yards in front of me. Im trying my best not to spook her off as Im trying to get pictures of her and the birds around me. I notice after clearing some brush to my right that another doe is walking along the opposite shore of the pond walking in the same direction. i stop to take a few shots of her but she is a bit out of range, roughly 40 yards, for my lens to get a good shot so I continue with the doe right in front of me. Suddenly I hear an immense WHOOSH coming from the pond to my right and as I look over I see the previous deer coming down from about 10 feet in the air and take off running, the deer in front of me also makes haste to get the hell out of there. I see on the opposite bank, a large amount of water retreating back down the shore into the pond. As the water clears there on the bank in a clearing is a HUGE gator, probably 12-16 feet long and easily several times my weight. My heart was pounding and seeing as I was only a few feet from my side of the shore of this pond I decided to continue my walk a little further away.
This is the deer I was following
This is a smaller gator I shot that day, I was too nervous to try to get a good shot at the first one.
I once saw a crow or grackle come flying through a clearing in the trees as fast as he could with a bald eagle in hot pursuit. The eagle quickly closed the gap and snatched the black bird from the air, only to tumble towards the ground, end over end for a couple seconds, while struggling with the other bird. about ten feet before hitting the ground the eagle spread his wings and flew off with his prize.
I once was photographing a Red Shouldered Hawk that was perched in some dead fall across a river mouth from me(roughly 45-50 yards). I was getting disappointed with the distance and my ability to focus on it from that far away when suddenly he started to fly in my direction with some serious purpose. The closer it got the more i started to get a little worried, it was flying RIGHT AT ME. As soon as the bird got to me I ducked and could feel the air turbulence from his wings. The hawk landed in some marsh grass about 10 yards behind where I was sitting, and he wasn't going anywhere fast. I couldn't see where he was but knew he hadn't flown off just yet. I crept around the brush that was blocking my view only to see him tangled up with a snake both fighting for their lives and a days meal. This really showed me the visual acuity these birds actually have. The picture below is the best of what I got from that.
Last one for now, I happened to walk up on this Coopers hawk eating a galinule in the parking lot at school. He was not about to leave me with his catch but could not lift him to fly off. he just kept staring at me and eating. I got to within 10 feet from him crawling on my toes and elbows so as not to scare him. I had only a small lens with me but he let me get close enough to get some great shots. I could hear his beak breaking through the bones and ripping through flesh and feather while i sat there shooting this guy.
Some people get their nature from discovery channel, some of us go out and find it.