The Pacific Northwest is famous for the prehistoric Sixgill Shark, which hasn't changed since the Triassic period. These deep water sharks rise up to diveable depths when the plankton blooms keep the light levels low enough to avoid blinding their light sensitive eyes.
Local divers also frequently run into the "little varmint" of the sea, the pesky Spiny dogfish shark. They like to buzz divers, and I've had them bump me a few times, which is un-nerving when you don't see them coming.
The Galapagos Islands are famous for its female Whale Sharks. These gentle giants of the open ocean cruise the currents around Darwin Island filtering plankton from the rich waters there. Whale Sharks should be on your "must see" list as a diver.
The Hammerhead sharks of the Galapagos are also incredible. They are scared to death of divers, so you have to hold your breath and hide behind a rock to get close enough to take a pictures. They do look a bit like someone made a mistake.