The worst I have heard is one guy who got his face bitten off after hugging and kissing a nurse shark. He lived, though.
I’ve scuba dived with sharks, or rather dived places where sharks turned out to be. While diving on my honeymoon a hammerhead swam right behind me and I missed seeing it.
Honestly, I wouldn’t do it for the same reason I don’t swim with dolphins (or feed the bears in Yellowstone or pet the chimps in Kenya.) Wild animals are better off if they don’t get accustomed to being around people - especially if there’s food involved. It would be bad for the sharks if they got the idea that small boats full of people = food.
I can’t help wishing for it though.
I’ve had blue sharks approach within about 10’ during dives in the Virgin Islands. Saw a tiger shark in Hawaii (Big Island) that didn’t seem very curious.
I hate when that happens.
I hate animal prints. Besides, I’ve heard a rumor that you still “go” in the water – I thought you were supposed to stay in the kiddy pool if you did that.
I might do the cage dive thing if there were lots of other tasty targets around 
and people weren’t doing dumb shit like teasing the sharks or getting too close to them. I’m thinking more along the lines of everybody hangs out in the water and watches the sharks in a relatively controlled setting with escape and rescue options. I would not do a wild, unfed, unknown shark swim (presumably the captive sharks know the routine and are used to having people around, at least to some extent).
My objections are along those laid out by Merneith, and also ones of self-preservation. My opinion as a relatively risk-averse person is that it would not be worth the (probably small) risk of getting hurt. I know that shark attacks are VERY rare compared to, say, driving, but I do not trust wild animals with strong predatory instincts, and it would only take one shark incident to ruin my day. Working with horses, a domesticated and thus supposedly very safe animal, and nevertheless getting minor injuries and seeing other people get seriously hurt, I have come to realize that there is no such thing as an animal that you can trust 100% and be able to predict its reactions, even if you have known it its whole life. With something as big as a shark or a horse, I can not see taking unnecessary risks. These safety concerns are just MHO and apply only to me and not to what the braver or more motivated people decide to do, as long as the sharks are not unduly affected.
If you’ve spent much time in salt water, you’ve probably been much closer to sharks than you realize. I’ve seen six feet long hammerheads and tigers within fifty yards of the shore in water about six feet deep. I don’t swim in the Gulf anymore; I pushed my luck enough when I was younger.
The different responses to this OP correlates/indicates pretty clearly a significant difference between respondents: whether they’re scuba divers or not:
- Most scuba divers (with some dive trips under their belts) not only are not afraid of sharks, but consider it a treat to see them on a dive (no cage, no protection).
- The majority (big generalization, I know) non-divers consider all sharks to not only be dangerous, but naturally aggressive.
There are some 90+ species of sharks in the oceans, and of those only something like 5 or 6 are known to be aggressive to humans. And “aggressive” doesn’t mean “hunt them out whenever they smell humans in the water”, but rather there had been “incidents” (among the 100’s of encounters that were incident free).
In case you hadn’t guessed, I am a diver. And I have been in the water with lots of sharks:
reef sharks (carribean, white tip, black tip), “wussy” nurse sharks (although I have video of one munching a parrot fish, and it did not appear all that “wussy”), leopard sharks, horned sharks, whale sharks, and 100’s of (the dreaded) hammerhead sharks. No cage, no chain mail. Never an incident. Never even any “aggressive” moves.
So for all the non-divers, here’s an interesting tidbit about these “dangerous man-eaters”: most of the ones you encounter are afraid of your bubbles (including the hammerheads) ! Most things underwater are not too thrilled with your bubbles, and sharks are no different. This is the trick you learn to get close to take pictures - you time it with your exhales to be able to not scare them away.
I am another who is both fascinated and terrified of sharks.
I snorkled in Okinawa knowing full well that humongous great whites had been caught in the very spot I was milling about, which is kind of surprising in retrospect. If I had actually seen a great white, much less been anywhere near one or been accosted by one . . . well, to borrow from Bill Bryson
After that? I’m NEVER cage diving.
The knowledge that I’d be very unlikely to be attacked, regardless of the type of shark I was swimming with, wouldn’t stop me from being scared.
One of my goals in life is to invent the sport of Shark Rodeo.
Thanks a lot; now I can never go swimming in the Gulf of Mexico again. 
I grew up in Houston & Galveston when I was young, and the Galveston beaches were the first beaches I ever swam in. We still go there when we visit family in Houston.
However, I also have this real terror of sharks. I think it was because of Jaws. Not the movie (my mom wouldn’t let me go, because I was too young); no, I read the book. That was enough, apparently.
Yeah, I think that I would probably be OK if I was diving. If I were scuba diving underwater and could see what’s going on, I don’t think it would be as terrifying as bobbing on the surface with no idea what’s below you.
I just watched a couple Youtubes of cage diving where the sharks get partially in the cage. One question- WHY are the openings in the cages so big? The last one I watched the shark was 15 feet long… that is a BIG shark Wouldn’t it be safer to have smaller openings?
To answer the original question- I would LOVE to dive with sharks in a cage if the openings were smaller LOL.
The feeder never gets attacked, and the other fish never do either, because the sharks are offered food 10x as often as they eat in the wild.
As for swimming with sharks…only really small ones. Animals bigger than me, including horses, make me uneasy to get up close and personal with. If the shark is only 3’ or 4’ and overfed, yeah, I’d swim with it. I’d be more afraid that I’d be accidentally drown by a bigger one than bitten, though.
I would need a brown wetsuit.
Cool. I happen to be in Exmouth tonight. Did you go for a snorkel at Turquoise Bay? It’s common to see black and white tipped reef sharks there and I’ve seen a grey nurse as well. I also had a swim at the Cocos (Keeling) Islands a few weeks ago and saw a small reef shark. I’m generally pretty comfortable around sharks who don’t appear to be aggressive (when I first saw a shark while snorkeling I told myself “all these other fish don’t seem to be scared, why should I be?”)
I think, on the question of doing a cage dive with a great white with chum, I wouldn’t do it. Not because of the fear factor, though I’m sure I’d be nervous, but I’m not keen on having wild animals made to perform for us. I’d do a cage dive with great whites if they were just left to their own devices and I could watch them swimming around naturally.
Hell yeah.
I do a website for my buddies in Thailand, and when they asked how they could pay me, my answer was: “fuck the money, get me in the water with sharks”. In 30+ dives I’ve not seen a single one. 
I leave next Feb… if I don’t post again here after then, you know what happened.
No one has bothered to try and answer my question- why are the openings so large in a shark cage? All the videos I watched, the openings were WAY bigger than I would be comfortable with. In one, it allowed a 15 foot shark to get in.
So, I ask, why not make the openings smaller?
I would never do this, although I am pretty sure I’d be safe. No shark would attack somebody surrounded by that much urine.
I can’t imagine why anyone would want to do this, but I don’t get death sports anyway.
That sounds like a Siegfried and Roy incident waiting to happen.