Sharks have a 10% chance of dropping a Shark Egg when killed. In order to get a tamed Shark, you need to hatch this egg by throwing it into the water, which will hatch a friendly baby Shark. Once it grows big enough, it will attack other Mobs (like Squid). Tamed Sharks will not attack other Sharks or the player.
You can ride a Shark.
There is no current way to heal a tamed Shark by "feeding it" (as is possible with other tamable Mobs). The only way to heal a tamed Shark is to throw a Splash Potion of Healing at it.
Sharks drop Shark Teeth when killed, which can be used to create Chainmail Armor without the use of Fire or spawning it in. They can also be used to make a Shark Sword, a weapon unique to the Mo' Creatures Mod.