Those bones are called vertebrae so the animals are vertebrates. The animals that do not have backbones are called invertebrates. Some examples of vertebrates include human beings, cats, dogs, fish, elephants, and chickens.hose bones are called vertebrae so the animals are vertebrates. The animals that do not have backbones are called invertebrates. Some examples of vertebrates include human beings, cats, dogs, fish, elephants, and chickens.