About once every three minutes. That, according to my rough calculations, is the average amount of time I can spend in a crocodile or alligator exhibit on a busy weekend before someone in the audience - almost always, though not exclusively, a middle-aged man - makes a comment about alligator wrestling. Usually they'll ask jokingly if that's what I'm about to do, sometimes they'll make an offer to do it themselves (thereby impressing their female companionship). There's no avoiding it.
Perhaps most annoyingly, to me, anyway, is the fact that so many of them say "wrassle" instead of "wrestle." A small source of irritation, considering other things, but I was raised to be a stickler for correct grammar and pronunciation (hard to believe, considering how many times I have to go back onto the blog each day to correct typos).
As legend has it, the first alligator wrestles were the Native Americans of Florida - the Seminole, the Miccosukee - who hunted alligators for meat and hides; later, alligator products became useful trade objects with European-Americans. As is the case with so many native skills, it eventually made its way into the tourist trade, performed in attractions across the south. Crocodile Hunter, Swamp People, and other TV shows greatly enhanced its popularity.
In the strictest sense of the word, I've wrestled alligators and crocodiles before - if by that, we mean that I've gone and captured them bare-handed by myself. Not especially large ones - my rule of thumb has been not to catch an alligator longer than I am tall without back-up, and the capture of the larger ones usually involve some rope and tape. Also as a rule, I do it when I have to, not when I want to (which, to be honest, is far less often than I have to). It's done for husbandry purposes, such as medical treatment, or for emergencies (such as moving animals inside in the face of sudden, severe weather that might compromise the integrity of the exhibit).
In the case of an alligator less than six feet long, it's usually a matter of just grabbing the animal by the back of the neck with both hands, coming up from behind and using my body weight to hold it down. From there, I can grip the jaws closed (the muscles that open a crocodilian's jaws are pretty weak, and I can easily hold even a big croc's mouth closed) while electrical tape is used to secure it. Bigger animals need a team effort, maybe using a lasso to secure the jaws, another for the tail, and two or three people to hold the animal down. It requires a fair bit of coordination, as well as trust in one another's abilities. When you're rushing to jump on the back of a fifteen foot alligator, you really don't want to be worrying about whether the two people behind you are actually coming or not.
There really is no equivalent of this in mammal keeping. If you told me that I had to take two or three keepers and go into an exhibit with a polar bear and wrestle it into submission, I'd probably just as soon shoot myself in the head and get it over with - there'd at least be more of a corpse for burial that way. There are some facilities with lots of crocodilians which are masterful at doing these captures (St. Augustine being the golden example, I suppose). Some zoos may go years at a time without needing to do this.
Catching alligators and crocodiles is stressful for the animals as well as the staff. It's best if it is done quickly, quietly, and efficiently by a trained staff. Whenever given the option, I try to avoid doing it during public hours. I'd worry too much that I'd be distracted by the public and make a mistake that could result in injury to me, or the animal. So no random guy in the audience, there won't be any gator wrassling demos today. Or any day, actually.