Having dove with sharks all over the world... Tiger, Hammerhead, Bull, Sandtigers, White Tip and Black Tip Reef, Grey Reef, Nurse and Thresher, I have the following tips...
1. If you see an Oceanic White Tip, Great White or Tiger, it is recommended that you get out of the water if you are by yourself, are in limited visibility or are simply not comfortable being there. We still believe that sharks, like dogs and other animals can sense fear and it may lead to signs of aggressive behavior. These three sharks present an imminent risk.
2. When diving with Bull sharks watch for aggressive behaviors. With Bull sharks this tends to start with circling you at a distance, gradually circling closer and leading to a bump / bump and bite situation. Generally Bull's can be very territorial and may simply want you out of their area. I have personanly encountered a circling Bull... and once I got out of his area, he did not pursue or show any other signs of aggression.
3. Sandtigers can be approached closely and even followed safely... but do not touch them. Be cautious in photographing them. Some are known to have a quick and nasty responses to camera flashes. Otherwise enjoy your time with these wonders.
4. Hammerheads are graceful animals that usually pass by without any interest in divers. Do not chase or try to touch them. They have proven to me on occassion that human food can lead them to turn and come at you... so don't take any food in the water when Hammerheads are present.
5. Generally speaking all of the common reef sharks around the world are safe to dive with, even during feeding. Grey Reef, Carribean Reef, White Tip and Black Tip Reef are generally not aggressive. If they do exhibit aggressive behavior it will be obvious. Swimming speed increases, jerky body motions and the pointing down of fins. If these are being exhibited, it's time to get out of the water.
6. Nurse sharks are one of the most docile and playful sharks, but do not mistake their power. I have had them grab my fins and shake them playfully and I have been able to safely pet them (wearing gloves) without consequence. Do not attempt this with a sleeping shark (do not startle them) and unless you are prepared to be bitten and willing to accept that risk - don't try it at all. They have powerful jaws made for crushing.
I do not have experience with any of the other species and don't want to make blanket statements except these few. All sharks - even small ones should be considered dangerous and you should always know where they are when you're in the water with them. While they are potentially dangerous, divers have proven that they can be interracted with very safely. In other words, you can swim with sharks and not get bitten, but don't try the same thing with Lions on the Serengeti. Bottom line is be prepared for anything and enjoy the thrill of swimming in the open ocean with one of earths most beautiful animals.