No, all animals do not have skeletons. Only animals considered vertebrates, such as birds, fish, amphibians, mammals and reptiles have skeletons. There is a much larger group of animals called invertebrates that do not have internal skeletons.
Invertebrates far outnumber vertebrates. Ninety-eight percent of all animals do not have a backbone or skeleton. Insects are one of the largest groups of invertebrates, but other animals that do not have an internal skeleton include worms, crustaceans like shrimp and crabs, and mollusks, like squids and snails. Invertebrates may have a hard shell called an exoskeleton. Vertebrates are generally much larger than invertebrates.