@Great Argus , they certainly are a common species, but one I've never gotten the chance to work with. Weirdly enough, a month or so ago I stopped by the pharmacy after work, still wearing my uniform, and an employee there approached me to ask if our zoo had any hyacinth macaws for sale. He said owning one was his dream. I had to explain that a) we don't have that species and b) not how it works. Or at least not how it's supposed to work...
As to what
@Batto has said, the most neurotic birds I've ever worked with have all been cockatoos. The difference between macaws and cockatoos for me, however, is that I've never worked with a "normal," emotionally and socially healthy cockatoo, whereas I have with macaws, which has made the difference more jarring with those birds. I think it would be of major benefit for a zoo to do an exhibit of umbrella cockatoos to show an appropriate environment and social group, since so few people ever actually encounter them in one.
I'm trying to skip across taxa to keep things lively, and so having done two mammals and two birds, we'll hit our first reptile.
I've worked with five species of crocodilian over the course of my career, and it probably won't surprise anyone that the species I've worked with the most is the American alligator. I've worked with this species at three facilities - two non-AZA, one AZA - with individuals ranging in size from 1 foot to 9 feet long, in both educational ambassador and exhibit animal roles.
The thing that strikes me the most about American alligators is how inherently tough they are. This is an evolutionary blessing for them. It's also something of a curse in zoos. I used to joke that the only way you could kill an alligator was a shotgun to the head - in terms of husbandry, they're virtually indestructible. I exaggerate, of course, but because alligators can survive some pretty awful conditions, seemingly in good health and without obvious behavioral problems, they can sometimes be encountered in some pretty atrocious living conditions. The fact that reptiles tend not be very expressive doesn't help, as they have fewer obvious ways of expressing their discomfort, especially to those unfamiliar with them. The fact that they are not protected under the the Animal Welfare Act doesn't help (though there has been some noise about extending the AWA's protections to ectotherms as well).
I've only ever vomited at work twice in my career. Once was when I had a stomach bug but was still forced to come to work by management, and then threw up while cleaning the tiger dens (to be fair, the entire rest of the staff had the same bug as well). The second was when I started work at one sketchy roadside facility early in my career and saw the living conditions of four juvenile American alligators. They were in a plastic trough with a piece of hog panel over the top, submerged in a liquid that probably once was water, but by the time I saw it (and, more importantly, smelled it) was a mix of feces and liquified rodent. That facility, incidentally, set my record for shortest-time-spent-at-one-zoo. It was an extreme example, but I still am amazed when I see alligators in too-small, too-plain enclosures, no or inadequate lighting if indoors, incomplete diets (i.e., just chicken pieces), and so on.
(Side note: A personal choice that I've made, based in part on experiences with American alligators - don't get a reptile with the assumption that you'll only house juveniles, and that you'll be able to pass it off somewhere else when it gets bigger. I've seen too many places get small alligators for educational animals, or animals for smaller exhibits, then send them off without too much of an inquiry as to what happens to them. There should always be a plan for full-life care. St. Augustine used to have an arrangement within AZA that they would provide youngsters, and then take them back when they got too big and provide new small alligators to take their place, but I believe that they have since discontinued this service).
A better living situation was enjoyed by two adult female gators that I worked with elsewhere with a yard attached to an exhibit building, allowing the animals to be easily moved back and forth as the weather changed (I could just leave the door open when the weather started getting cold and they would generally shift themselves in). The exhibit was still smaller than I would have liked for them, but it was acceptable, outdoors for most of the year (so natural light, varying environmental conditions and substrates), and was kept clean and well-maintained. The diet was originally a rotation of fish, chicken, and rodents, before I switched them over to Mazuri Crocodilian Chow. Each piece looks like a charcoal briquette (which is also sort of what the alligator poop looks like). It feels greasy and gritty; you look at the piece of biscuit in your hand, look at the alligator, and scoff, thinking the gator will never eat such a thing. That's what I certainly thought. The joke was on me - they actually loved the biscuits much more than the conventional prey items; the biscuits floated in the pool, the gator would chomp at it and miss, causing the biscuit to move ahead in the water, and the gator would chase after it. The only problem was that they only really liked the biscuits when they were relatively freshly tossed - if a biscuit was in the water too long (and in my experience they would only eat them in the water), they'd loose interest in it, and it would swell up to a soggy mass the size of a brick. The grease from it would then form a sheen on the pool; I usually made a point of feeding them heavily the day before pool cleanings. Feeding occasional large prey items, such as rabbits, was good for enrichment, as well as promoting the strength of the jaws (zoo-housed American alligators often have weaker jaw muscles than wild ones).

Feeding some alligators at St. Augustine. The brown nuggets in my hand are Mazuri Crocodilian chow.
We worked free contact with our alligators of all sizes, no real difficulties encountered. The ones that made me the most nervous were the ones I worked with in the five-foot range - they were the little spitfires, full of vim and vigor, who would rush you when hungry (a five-foot gator is also about the size limit of what I'd comfortably grab by myself). Bigger gators were, as a rule, more serene. Visitors were always amazed to see us in the exhibit with the gators; some would walk by as soon as they saw us in there, assuming that if we were in the exhibit, there's no way the alligators would be as well (other folks, conversely, assumed we went in to groom the big cats daily...). The most dangerous thing about a large American alligator in a zoo is how easy it is to treat it with contempt, to assume that it's just a lump that's never going to move and that you can ignore. Even a large alligator that's normally docile and still can surprise you. This was driven home to me one day when working with the two larger gators. I'd decided that the substrate around the pool was looking kind of compacted and tired, and I wanted to add several wheelbarrows of dirt and mulch. They. Did. Not. Like. The Wheelbarrow. That or they really liked it - either way, it was bad news for me. I barely got the first load out with the damn thing intact. When I came back with the second load, both were at the door of the exhibit, hissing like steam engines, trying to push down the door to get to it. After that, I only was able to do one load per day, sneaking it in and rushing to get out before they charged out of the pool and tried to seize the wheelbarrow and drag it in with them, for whatever purpose they had in mind. I've heard other folks say they've had similar experience with lawnmowers (which I have not encountered), presumably because the noise reminds the gators of a rival (alligators are the most vocal of reptiles, with vocalizations ranging from bellows - usually the bulls, but cows as well - to the little chirps of the hatchlings, which begin before they even hatch).
Alligators are surprisingly cold tolerant, and at one zoo I actually saw a few gators with their snouts sticking out of the frozen surface of their pond. All of these factors - cold-hardiness, impressive size, relatively docile nature, and easy care (to say nothing of how easy they are to acquire) - have made American alligators the most popular crocodilians in American zoos. They'll obviously always have an important role to play in native wildlife exhibits in the southeast, but it would be great if more zoos - especially those with indoor exhibits that are not restricted by zoogeographic theming - would take a risk and work with the more endangered species prioritized by the CAG. Speaking of which...

Target training an American alligator. There were two female alligators in this exhibit - one was targeted to a purple square, the other to a yellow triangle. I noticed that the animal targeted to the yellow triangle always closed her eyes when she approached the target - I wondered if the color was too bright/irritating for her. Notice the clicker under my thumb. I did this training to help get the largely sedentary alligators moving more often in order to lose weight.
Besides the Americans, I have two zoos of experience with their close relative, the Chinese alligator. Compared to Americans, Chinese have a reputation of being more pugnacious. In my experience they're much more shy. At one zoo, I could only check on the gator by watching it from well outside the exhibit; as soon as I started to put my key in the lock, it immediately went into hiding, and all I'd see of it when I went into the exhibit was the part of its tail that couldn't fit into the rock crevice that it hid in. I was able to habituate and eventually make "friends" with this gator, to the point where we were able to train for some basic behaviors, including scale trainings and even entering a trashcan so I could safely remove it from the exhibit. Brain size and intelligence are not the same thing, of course, but it amazes me how intelligent alligators and other crocodilians are, and to what an extent they can learn.

My plucky little Chinese alligator, who used to hide from me every day, posing comfortably out in view a few feet from me in his enclosure after only a few months of work
One last note on alligators. I'd be remiss if I didn't mention one of the most amazing professional development experiences any reptile keeper can home for - a chance to attend Crocodilian Biology and Captive Management at St. Augustine Alligator Farm, or, as it's usually called, Croc School. In this week long course, students study every aspect of crocodilian care in the living classroom that is St. Augustine, from sexing hatchlings to performing a necropsy to running a training project with young alligators. It was this course which really made me re-evaluate how we'd been taking care of crocodilians (and where I learned about the Mazuri chow, and much of what I know about crocodilian training and enrichment). The course even has a field trip to see gators in the wild, as well as an animal capture workshop, where teams of students work together to capture and restrain some of the biggest crocodilians in the park (my team had a 13 footer!). An amazing learning experience all around, taught by some of the most knowledgeable folks n the field!