Looong time ago when I was in college my Dad met me to fish Red Bank Creek fly section near Brookville.  Don't remember the fly but in a fairly open area as I moved my rod forward from short backcast it stalled.  Not only stalled but hung in the air. I'd managed to hook a hummingbird and for a short while he was actually able to keep my line aloft. Only lasted for a short time before he came down. We released him and he flew away apparently unharmed. Over 25 years ago and every once in a while it still pops up in conversation. 

I caught a duck on corn once, nearly caught a few more on bread. I've also caught bullfrogs on topwater frogs, I've seen people using Joe flies dangled right in front of a bull frog to catch em too.. My wife caught a softshell turtle on half a blugill w a shell about 20" across, that thing was mean! Also a few water snakes in my minnow trap from time to time.

Caught a hellbender through the ice on the Clarion river when I was a kid, also caught a used condom once  didn't fight much though...

caught a bat fly fishing at night on wolf creek
a loon trout fishing in stoney creek
a beaver while salmon fishing up in NY and
about 10 years ago some dude who stepped into coolspring creek in flood water only to invert and go downstream legs flailing away as he tried to turn over...i must admit i snagged him though
 
i used to catch turtles for a local resturant back in mercer as a kid so snappers are kind of a given for me

fishing Donegal lake last summer thought I snagged a big weed ball but it kept feeling like it was pulling back real slow. Eventually pulled it up to the side of the boat and this guy was on the end of my line.

Wanted to try to get my lure back, but decided I like my hand more than I liked that lure.

Never did catch him but I had a duck chase my silver/blue Kastmaster about a half dozen times one day at Justice Lake. I was trout fishing on the dam and the little duck would dive underwater everytime he saw where the lure plopped in the water. He drove me nuts I had to wait till he wasnt watching so I could cast....lol. I did even manage a few nice trout that day.
 
The weirdest thing I ever caught was a mudpuppy/hellbender in French Creek one day using a crawler **** thing was probably 20 inches long. I was just a kid and had NO idea these things even existed in the creek, Yep I was scared 

Managed to catch myself while smallie fishing on French Creek last year.  Buried a treble hook in the pinky on my left hand.  My buddy had to walk away from me as I swore, laughed insanely  , and shoved it the rest of the way through so I could cut the barbed end off.  Its amazing how hard it is to push a hook through 1/4" of solid flesh.  Only after the fact did I read anything on proper removal of a hook.

Couple of weeks ago I caught a boat, or rather a jacket that was IN a boat that got a little too far inside my casting range.

i didn't land him but i did hook a guy up on the salmon river this year that insisted on wading out to the exact spot i had been fishing for a couple hours....i asked him nicely to move....he didn't, i kept fishing, felt something move and set the hook into his thigh
 
i also hooked my own ear with a size 2 fly, on a windy day....not a good way to get a pierced ear

Caught a 16oz cottage cheese container in 16 fow a few weeks ago at pymy If anyone lost please contact me. I kept it in case anyone came forward....Please provide accurate description.
 
Thanks, Joker