So far, scientists say that the Thylacoleo carnifex, a marsupial lion that lived in Australia during the Ice Age, had the hardest bite ever. When scientists discovered this, they also found out the animals with bigger brains have a weaker bite. So it is rather clear this fierce biting mammal wasn't very bright. It has been extinct about 40,000 years, so you won't have to worry about having them roaming around your neighborhood.
Alligators have the strongest bites of currently living animals. The second strongest bite is owned by alligator snapping turtles and common snapping turtles.
Scientists are also saying that the great white shark has the strongest bite force so of today's living animals, it seems to be a toss up between the great white shark and the alligator.