A snake does have a backbone. In fact, the majority of bones in a snake's body are vertebrae, the cylindrical bony segments that make up the backbone or spine.
Snakes can have anywhere from 130 to 500 vertebrae, depending on species and length. The vertebrae have interlocking projections on the front and back ends to allow for a combination of flexibility and strength. Unlike other animals, snakes use their vertebrae as their primary means of locomotion, rather than using limb bones. Most snakes wriggle their spines in a smooth, S-shaped motion called lateral progression in order to get where they're going. Heavier snakes move their spines up and down in what is called rectilinear motion.