I guess the only one I can think of is the sea otter…I’ve seen wild ones in Valdez Alaska.
Plus of course, bears, moose, caribou, sheep, foxes, and so forth, but those aren’t particularly rare. Never a muskox, lynx, cougar, wolverine, or anything really rare.
Since bald eagles apparently aren’t all that rare (judging from the sitings mentioned here), I’ll have to go with a Gila monster. On the one I saw, the orange was much brighter than the pictures on the Wikipedia page - they’re beautiful creatures, even if you don’t want to get too close.
When I was ten years old, I saw an albino rattlesnake in the woods near my grandpa’s farm. It looked very much like this snake. I’ve been fascinated by albino snakes ever since.
While you were flying or the whales were flying? 
Platypusses (?) are still quite common around my neck of the woods.
mm
That would certainly be rare, as the beluga’s normal range is in the far north:
Desert Bighorns in Anza-Borrego and at Flaming Gorge. Rocky Mountain Bighorns at Glacier.
Desert Bighorns here, too - at Joshua Tree, about 5 years ago. The rangers were pretty excited - they hadn’t been seen much during the drought.
A Yellow-faced Grassquit in Florida (not rare, world-wide, but certainly a biggy for Florida.) A tree-kangaroo at the Curtain Fig in… oh shoot, forgot the name of the park in Australia. Maybe not rare, but hard to see. Also, quite a few Bustards in Australia - I guess we found out they were unusual after we saw them.
Haha. The Hawaiians WISH they were rare. There’s a mongoose problem in Hawaii. Something like they were brought over to control the rats, then became a problem in themselves. There was a little mongoose family living near Manoa Stream close to where we lived in Honolulu.
I saw a pair of Purple Martins the other day at a special nesting area at a local garden.
Not really rare except in the greater St. Louis area where their numbers are decreasing at a extreme rate.
My three rarest sightings all come from a mis-spent youth in and around Florida’s Everglades.
1)Everglades or Snail Kite. Thought to be about 300 of them in the 1960’s.
2)American crocodile. Probably less than 50 adults in the wild when I found a nest. (early 1960’s)
3)Florida panther. Not very many at all. 40 or so?
Yeah, they’re the top of my list too - I saw one on Santa Cruz in 2004 and it was quite cute.
Other animals that have made the list:
Southern Sea Otters (only slightly more than 2,000 left)
West Indian Manatees (about 3,000 left)
Blue Whales (I work as a whale watch naturalist on weekends, so I better see 'em!) - about 8,000 to 14,000 left
Humpback Whales (about 30,000 to 40,000 left)
Grey Whales (about 20,000 left)
Risso’s Dolphin (not really rare, but people don’t see them often unless they go offshore)
Guadalupe Fur Seals (7,000-8,000 left)
Peregrin Falcon (not sure how many there are)
I’d count Snowy Plover too - but I cheated - it was in captivity.
I’m really jealous Spiff - I went to Maui in 2005 and a friend of mine saw a HI Monk Seal, but I didn’t.
I’m also jealous of DrMemory - I tried to find California Condors at Pinnacles National Monument in 2005, and during several trips to Big Sur, but I’ve never seen one yet.
Must second the recommendation of Last Chance to See, it’s an excellent book!
Show up next weekend–I can almost guarantee a sighting: Condor release 2007.
Key deer - Wikipedia I have seen these critters twice. Most are like 30 pounds and german shepherds and other big dogs kill them a lot. Traffic kills them too.
I’ve seen a relative of that fox on Catalina Island. They were endandgered for a while (I believe because hawks were eating them all up), but they were “re-introduced” by humans in a preserve (successfully, it seems), so I wonder if that really counts as “in the wild.”
In the same place, I saw a buffalo. For the same reason, I don’t know if I should count it as “in the wild.”
I saw a cougar (mountain lion, catamount, etc.) once from afar in southern CA. That was definitely in the wild, but they’ve been known to attack people in Orange County parks. I don’t think they’re particulary rare, but they’re extremely shy of humans.
Another interesting thing I’ve seen, this time in the Amazonas, was a sloth. Again, I don’t think they’re particulary rare, but they’re hard to see, because they just don’t do that much. Thre just hang there in trees and chew on leaves. But this one was swimming across a stream! I asked a friend if I could buy one and take it back to the States as a pet. He said, alas, that it would be illegal. Wouldn’t a sloth be a perfect pet? Just put it in a tree with a lot of leaves; when you want to share “quality time” with it, it will wrap it’s arms around your neck as though it were a tree branch, and go to sleep–after you give it a few fruit treats.
Then I saw a San Francisco Garter Snake, in San Mateo. At least, I’m pretty sure that’s what it was, because it had such beautiful, unusual colors. I tried to catch it, to no avail. After descrbing it to a snake person, she said that’s probably what it was, and that I should have left it alone, as it’s an endangered species.
I saw manatees outside a power plant in Florida once. It was on the east coast of Florida but I can’t remember what city.
I’ve seen the sea otters at Los Lobos Point south of Monterey, CA and bison at Yellowstone, although they’re not really uncommon there. I’ve also seen Whooping Cranes and Trumpeter Swans.
I saw a swift fox in New Mexico once. Unfortunately it had been playing tag with traffic on the highway and lost.
I worked with the New Zealand Wildlife Service from 1981-1985, and got to see some of the rarest animals in the world during my stint with them.
My favorite is the Kakapo, or Owl Parrot - a giant, flightless, nocturnal parrot. I worked with an island translocation program for them, and handled about 10% of the world population - which was about 50 in total at the time.
My own bird, which I was doing a study on, was the Stitchbird, or Hihi, at that time restricted to a single island, Little Barrier. I estimated the population at that time to be about 5000 birds.
Other species I’ve seen in the wild include Takahe, Saddleback, Kokako, Little Spotted Kiwi, and Tuatara.
A great book. Adams spent some time in the field with some of my NZ friends, including the Dobbins family and Kakapo-catcher extraordinaire Gary “Arab” Aburn.
You may have me beat. 
That could well have been at the Turkey Point nuclear plant south of Miami. The plant discharges (or did, I’m not current there) lots warm water into the bay, which attracted a number of manatees in the cooler months.
My mom has seen the pietated wood pecker. And yesteday she saw an osprey.
She’s a birder.
I saw a snake. Not too rare but it happened to be swimming right next to me :eek: I have no idea what it it was , I just swam in the other direction.
And then there were the bugs on my potato plants. I’ve never seen them anywhere before. And no-one can tell me what they are. I still want to know.
Bald Eagles, twice (DC metro area) - once in Lake Accotink Park in Springfield VA, and once in Charles County MD.
We saw a glimpse of a whale breaching off the California coastline during a drive north from Monterey to San Francisco, though we didn’t identify the species. And we saw sea otters near Monterey that same trip - not sure if they’re at all endangered though.
Just last night I got lost taking a walk in my neighborhood and saw an armadillo.
