Mr. Dibble already mentioned Penguins, but as he didn’t say what kind, I"m going to assume Black-footed penguins (formerly called Jackass Penguins).
I’ve seen Adelie penguins, Emperor penguins, Fjordland Crested penguins, and Yellow-eyed penguins, but I think the coolest I’ve seen was a colony of Snares Island Penguins.
Xema’s post reminded me that I"ve also been lucky enough to have seen Takahe in the wild. I was on a research project that flew into the Murchison Mountains, and followed a few pairs around for several days. I still have some great photos of birds with no leg bands - a rarity I think since there are only 200 of them in total, and most are banded!
Northern Florida, both west and east, is brimming over with wildlife. Many/most of these would not exactly be considered exotic, but some of them have turned up in unusual places. Most of them were sighted within blocks from my house, if not closer.
In the wild, I’ve seen, (most quite regularly) gators, bald eagles,osprey, grey fox, sea turtles, manatees, river otter, armadilloes, bobcat, wild hogs, 'possums, sting rays, dolphins, ibis, pileated woodpecker, indigo bunting, spoonbills, bull sharks, right whales, black bear.
(Never the Florida panther, though.)
Saw coyotes on the northwest side of Florida. On this side, I’ve heard what certainly sounded like the yip-yip of coyotes, but never seen them.
When living in central Denver, I regularly saw a female coyote–once with a piece of pizza in her mouth.
Are they rare on the west coast? We see them on the SC coast several times a day in the summer.
When I was in Antigua some years ago (cows roamed loose around the island :rolleyes: - I wonder if they still do, now? ) I saw a mongoose in the wild. It was not rassling with a snake, alas…There are bald eagles that built a nest, by a lake, near the mall a few miles from my house - I got a glimpse of one, waiting in traffic on the way out.
Reminds me of visiting a muskeg island on a stagnant, swampy lake in northern Quebec. Now, that was wierd, at least to me - a floating island of vegitation you can walk around on (carefully!), liberally festooned with carnivorous plants - pitcher plants and sundew (which is even wierder).
A wood thrush.
Not very exotic, but rather unexpected: a fox running across my back yard. We live in the mountains, but I never knew those buggers lived here, too! XD
Orca.
Our summer cottage was in the Southern Gulf Islands in BC and “J” pod was/is the resident killer whale family. We were salmon fishing by East Point and, on our way back to the cottage, the pod started surfacing and spy-hopping all around our boat. I was sitting on the bow, with my feet dangling, and I could reach down and touch a fin when a whale surfaced beside the boat.:eek:
Sometimes they would travel down Tumbo Channel at night and I could hear them blowing as they surfaced.
Many years later, while visiting a friend in Victoria, she mentioned that she had never seen a killer whale. And her house was on Trial Island Passage. I said that the killer whales would come to see me and she laughed. Three hours later, the whole pod was going after herring in front of her house.
I miss J pod!
I grew up in a suburb of Portland, OR, which is inland. I think they spent more time in the northwestern bits of Washington.
Um, have to say a Wolf. When I lived in Texas and did a paper route. It crossed the road in front of my car at 4 am or so, (I stopped) paused, then went on its way into the overgrown empty fields. I had a long, good look at it in my headlights.
No-one believed me (no wolves in Houston…you must have been sleep deprived:rolleyes:) but I confirmed it on a trip to the local science museum soon after…they have a stuffed Mexican Wolf. Yep, that was it.
I know cyotes and foxes and dogs…this was a WOLF, dammit! :mad:
Aside from that, I’ve had the pleasure of encountering a lot of birds in the wild, from bald eagles to great blue herons to woodpeckers to owls. Oh, and once, a roadrunner. Cool!
Oh, those are so cool! Have encountered them in the wild as well, even bigger ones. And my son used to keep a tank of some of the Vietnamese variety (until I discovered the person at a local museum who gave them to my class should not have, as they were a controlled species…AND they reproduce like mad…we ended up having to commit genocide on the lot of them, rather than release any into the wild where they compete with native species for the rose and blackberry leaves they feed upon. :()
No bears, coyotes, wolves, or bighorns on my trip to Yellowstone, but lots of Bison, elk, deer, and bison. The 40 minutes stalking a bald eagle that was fishing in the Yellowstone river was time well spent, even if the pictures did not turn out nearly clear enough.
Saw many kangaroos and parrots in the wild while in Australia, besides the ones in the various zoos and wildlife preserves. Also quite a few wallabies and one dingo that came up to the parking lot begging for food while in the West McDonnel range. It doesn’t meet the OP’s criteria, but I have to mention the Little Penguins at Phillip Island Nature Park. They are unbelievably cute, and entire parade was wonderful to watch.
Mutliple species of tropical fish while snorkeling in Maui, but the unexpected part was the sea turtle that was in the cove also. It was actually rather intimidating when I got close to it, mostly because I was aware I was literally in its element. But still fun. The only part of that day that was a downer was getting back to the hostel that night and finding out some of the others there had been at a beach a quarter of a mile from the cove I was in, swimming with dolphins. :eek: And they had asked me to join them when we were leaving that morning. :smack:
The most majestic, for sure: Gray crowned cranes in Michigan, once flying over calling while I was in the woods, and on another occasion just standing around outside the library in a suburban area. I don’t know how exotic they are but they’re definitely impressive.
Sea elephants on the California coast.
Roadrunner. Shouldn’t count as exotic because I live in Arizona, but I’ve only seen one so I was in awe.
A hippo, near Lake Kariba in Zimbabwe. (Also saw them in Krueger national park but that isn’t wild.)
Where was this? I’m guessing Cana. And who was your crazy Panamanian guide? I know most of the crazier ones.
I had an encounter with a jaguar in 1979 not that far from Cana, on Cerro Pirre above the town of El Real, although I didn’t actually see it. I was camped in a tent with a friend while our Indian guide was in a lean-to outside.
A little after dark we heard a deep grunting cough about 20 feet away from the tent. I asked the guide what it was. He said “Un tigre” (A jaguar.) I was sure he was kidding me. I said (in Spanish), “C’mon Jose. That sounds like a night bird to me.” He replied, “No, es un tigre. Esta cazando. Tengo mucho miedo.” (No, it’s a jaguar. It’s hunting. I am very afraid.)
For the next half hour or so we listened as it circled around the tent, keeping about twenty feet away, grunting all the time. The next morning we found its prints in the trail near our camp.
The best animal I’ve actually seen in Panama is a tapir, which I scared up from where it was sleeping near a trail at Cana. It went frantically galumphing off into the jungle. I’ve also seen Harpy Eagles several times. I’ve seen Tayra quite a few times, but not recently. They’re pretty cool.
A dead baby giraffe in Lake Conroe, Texas. 
I’ve visited a taxidermist’s myself, but I doubt that counts.
warthog family, mom and a couple of babies trotting across the road, Vilseck, Germany
African Penguins, more correctly, but yes. Also 1 rockhopper (like a Macaroni, but smaller), but that was at a cleanup of oiled beaches and so not totally unexpected, although they’re rare transients here.