Polar Bear on the Hudson Bay coast in northern Ontario.
I'm Indigenous and I've gone hunting and trapping with my relatives a few times in my life. On one of those trips we happened on a polar bear on the mud flats of the bay during the late autumn. We drove by in our freighter canoe (a very large oversized canoe with a 60 HP outboard motor) and the bear swam near us and then walked by a few hundred feet away. It wasn't afraid but we were. We watched for a while and then fired rifle shot into the mud next to it to scare it away. From the moment it started to run to the point it disappeared as a speck on the horizon was about a minute or two. I went up later to look at the prints and the clay mud looked like a tractor had driven over it. I couldn't believe how fast it could move on the mud. I quickly sank in my boots and could barely walk around.
One paw print was about the size of my head. I never left camp without someone nearby or a rifle in my hands.
Seriously! They're the biggest land carnivores bar none. If you're 5' - 5'6" a bigger polar bear will be able to look you levelly in the eye while on all fours* and on its hind legs, it'll be more than half your height again.
I saw takahē in captivity too, in Zealandia. You can sort of see why they almost went extinct - their big defence move is to sit reeeeally still. Big silly chooks.
Uhh, in the wild? I've seen some pretty uncommon wetland birds a number of times. Some pretty weird bugs too, although it's hard to say what they were.
I've seen big moose really up close, and that was epic, and would have been terrifying if there wasn't usually a car-stopping amount of wood between us. They're not rare, though, just shy.
I got a brief but good look at a wild Jaguarundi in south Texas nearly twenty years ago. I thought it was a bobcat at first, but it turned so I could see its tail and profile, and there was no mistaking it.
I traveled to one of the most remote places on the planet, drove hours on dirt roads, hiked another hour through deafening wind, and then crawled on my stomach to the edge of a a 1300' cliff, and hung off of it it just to take a picture of a puffin with my cell phone.
Well that need the disclaimers of "outside a zoo" and "of which i was aware of", but probably Hummingbird hawk-moth, it might not be very rare, but i was like "wtf a hummingbird in Poland?" and i managed to get close enough to see it's in fact a moth.
A wild beaver like a few miles from my house, and not a nutria, a real life flat-tailed beaver toothed fucking beaver. I was going to an artificial dam I use as a fishing spot and there he was. It was way bigger than I thought but I didn't want to disturb it so I turned around and went home.
In captivity? An Okapi? A rhino? Idk man I've been to many zoos and exotic zoos where you drive through and idk about the rarest.
About a year ago my wife and I did a zoo date and when we got out of the car there was this bird walking around the parking lot. Not sure what kind of bird, flew off after like a minute but I thought it looked really cool.
Either a black stork, a least weasel (actually pretty common, but difficult auf to see around here), Cerambyx cerdo (probably not as rare as most regulating bodies think), a Eurasian eagle owl (rare around Germany) or felis silvestris
Saw a fishercat in an industrial area not far from a large swath of floodplain and high voltage transmission lines. So there was a lot of territory for it nearby. Looks like a tall badger. Apparently pretty rare. Was walking around 18 wheeler trucks in motion like it owned the place, peeking around the dumpsters most likely looking for the young raccoons that hang around.