jeffnz: I've been lucky never seen any whilst diving, mind you I don't go looking either.
Sharks possibly the most beautiful things in the ocean. I've dived with black tipped reef sharks, a leopard shark, a bull shark and a whale shark. All without a cage. They are amazing creatures and seeing them in their world makes you appreciate the ocean in a way other people simply can't. I'm guessing seeing lions in Africa would be similar.
In diving it works very simply. Shark sites are known, they are safe as long as the person leading the dive briefs correctly and everybody actually listens. If you don't know how to dive with sharks such as not knowing threat behavior, don't do it.
If sharks relied on people for food, they would all have starved to death by now.
The thing that really makes the ocean dangerous is the water, most people who die in the ocean drown.