Many vertebrates have evolved limbless forms. Reptiles have on a number of occasions evolved into limbless forms - snakes, amphisbaenia, and legless lizards (limb loss in lizards has evolved independently several times, examples include Isopachys, Pygopodidae, Anguis, and Ophisaurus). The same is true of amphibians - caecilians, Sirenidae (a clade of salamanders that are limbless except for atrophied front limbs), Amphiumidae (a clade of salamander with extremely atrophied limbs that appear non-functional) and at least two extinct groups (Aïstopoda and Lysorophia). Legless forms of reptiles and amphibians probably evolved so as to be able to move underground or in water more easily.
There are also a number of fish with elongated bodies that have no or reduced appendage-like fins, for example eels and swamp eels. Hagfish and lamprey also do not have appendage-like fins, they may not have lost them, but simply retained the form that vertebrates had before they evolved limbs.
There are no known limbless species of mammal or bird.