The answer to this question is not as simple as it may seem. There are a variety of animals that can open their mouths extremely wide, but the one that holds the record for the widest gape is actually the snake. The snake's mouth can open up to 150 degrees, which allows it to consume prey much larger than its own head.
Other animals that come close to the snake in terms of maximum gape include certain species of fish, such as the barracuda and piranha, which can open their mouths up to 90 degrees. Some reptiles, such as alligators and crocodiles, are also able to open their mouths quite wide, although not quite as wide as snakes. And finally, there are a few mammals that are capable of opening their mouths surprisingly wide too - particularly some primates like chimpanzees and baboons.