Contrary to what you see at the movies, divers are not on the menu. That said, sharks are wild animals, even if they seem friendly or docile -- you don't pet them or yank on their tails -- but divers and sharks do peacefully coexist underwater.
Like RAD Diver, I, too have dove up close and personal with many sharks in the Caribbean, Florida and off Morehead City, NC. On one dive with Stuart Cove in Nassau, the sharks were so thick at the stern of the dive boat we had to time our giant strides carefully so we wouldn't jump in on the back of one. The Sand Tigers in NC are so docile they can be descibed as Barney Fife in an Arnold Schwarzenegger body.
Right after I got my C-card I did my first ocean dive in St Maarten and was very apprehensive about seeing a shark. I was so worried I might panic from fright and do something stupid. When I did see a shark -- cruising gracefully along the top of the reef 25ft away -- my response surprised me. Instead of being scared I was "Oh my gosh! He is so beautiful. Let's just stop and watch him a while!" I've loved diving with them ever since.
If you get nervous when a curious shark inspects you too closely for your comfort, just hit your alternate air purge button to let out a blast of bubbles. The shark will move away. Off Saba, a shark came out of the blue, swimming quickly toward me with pectoral fins down and back hunched up -- he must have been having a bad day. I raised my camera and snapped his pix. The flash from the strobe caused him to stop his charge and he veered off into the blue. I was never worried and you shouldn't ever be either. Just have fun. Appreciate and respect these wonderful creatures in their environment.