Actually, in the Caribbean & Florida, for example, most sharks you see are fairly small (under 6 feet) reef sharks, or nurse sharks. While either can inflict injury, neither is likely to do so (assuming you're not holding dead fish, trying to kiss the shark, etc...). Depending on the time of year you dive, and where, you might see a lemon shark or one of the other species I guess could be called 'mid-sized,' but I don't think any of the above warrant a fearful retreat from the dive environment. Look at the lemon shark aggregation dives out of Jupiter, Florida, and the wreck diving with sand tiger sharks out of North Carolina, where people dive with substantial numbers of roughly 6(?) - 10 foot sharks around them.
Then you've got bull sharks and large hammerheads. Big bulls seem to inspire respect, but I don't see people posting about exiting the ocean because they saw one. And outside of a shark feed situation, I'm not under the impression a group is likely to pop up around you. From other's postings I don't think big hammerheads tend to come around divers much aside from shark feeds?
Tiger sharks and great whites are the ones that inspire the most fear. Cageless diving with tiger sharks is relevant because it's very possible; out of the U.S., it's not far to the Bahamas, where live-aboard trips to 'Tiger Beach' offer a high likelihood of being in the water with tiger sharks, and out of Jupiter Florida some people diving with
Emerald Charters get to see them. I did a Jupiter trip last October and dove with Jupiter Dive Center, not shark fed dives, instead of trying to dive with Emerald Charters, as I believe I want to take some more time to 'grow into' that level of diving, and I am ambivalent about being in the water with medium to large tiger sharks right around me.
I can hardly imagine deliberately going into the water with a great white, no cage. Yes, in theory attack is highly unlikely, but in addition to the potentially massive size and sheer horrific majesty of a great white, there have been a number of accounts on ScubaBoard of whites 'messing' with people - circling, one mouthed somebody's scuba tank (imagine getting jostled & turning to see
that), etc... Here's a link to
'Who thinks this Sharks was Killed (or should have been)? Be mindful that's someone spear fishing.
Here's a link to a video of one showing up while 2 divers are descending the mooring line on the wreck of the
Duane out of Key Largo, FL. They're not spear fishing, the shark doesn't get close and isn't threatening.
One tip I've seen on ScubaBoard is to maintain eye contact with sharks. Try to keep yourself where you are looking at the shark, and it knows you are looking at it.
One other take home lesson from the above, from what I understand from others (I don't spearfish), is that while most recreational divers have little to fear from sharks in the overwhelming majority of recreational dives (e.g.: not shark feed dives, not chumming the water, not Tiger Beach, Bahamas or Seal Island, South Africa), the issue is different for spear divers. You might do a hundred recreational dives without seeing a shark, but if you take up spear hunting, it's way more likely you'll see them. Some may contend with you for your catch. Some spear fishermen believe you should (almost?) never 'let' a shark have your catch. Personally, I can't realistically imagine squabbling with a 10 foot bullshark over a fish, but that's just me.
Richard.