Animals that do not vocalize noises include snails, worms, hermit crabs, sharks and goldfish. Turtles, snakes, lizards and rabbits are considered silent pets because of the rarity of their vocalizations, though they are capable of vocalization.
Mammals have a larynx (voice box) and most birds have a syrinx, so they all are able to vocalize. The woodpecker is an example of a bird that does not vocalize but obviously still manages to make plenty of noise. Insects without a larynx or a syrinx, such as crickets and grasshoppers, can still generate noises by rubbing together their wings or legs.
Fish are also capable of uttering vocalizations, for example, the croaking of a catfish, though people rarely hear their noises from above water. Fish without any physiological ability to vocalize can also make popping noises by contracting muscles in their bodies. Sharks are considered silent, other than when they are eating; they generate a hydrodynamic sound when swimming quickly or changing direction, but they have no organ to generate a vocal sound.
Any animal with a heartbeat and a circulatory system cannot be considered a completely silent animal, because their circulation can be heard with the right type of microphone. A sea sponge, however, could be considered a completely silent animal.