Much like how Satan had originally been free to wander Heaven as an angel so to was the Serpent an accepted member of God's Earthly paradise (known as the Garden Of Eden) and was blessed alongside all other animals - it is believed that the Serpent originally walked on legs like other animals.
Yet just as Satan had caused rebellion in Heaven so too did the eternal trickster manage to cause rebellion in the Garden Of Eden - as punishment for what he had done to Adam and Eve, God removed the Serpent's limbs and cursed him (and presumably his descendants) to slither forevermore across the ground.
The Serpent is also occassionally believed to be another form of Lilith, Adam's original wife turned succubus - though this only applies to those who believe in that particular telling of the Biblical tale. According to this particular tale, after Lilith returned to the Garden of Eden to find Adam married to Eve, she vowed revenge by tempting Eve into eating the Forbidden Fruit, assuming the form of the Serpent (though she appeared as having a snake's tail from the waist down).
In Jewish lore and in the Sayings of Rabbi Eliezer, Samael, the Talmudic angel of death, was the Serpent. But after tempting her, he then seduced and had sexual intercourse with Eve, begetting Cain. But in some older Jewish legends, the Serpent, which was a tall and intelligent creature with human arms and legs, was created by God to be king of all creatures and eat the same food as humans. But he became envious of humans, which was the evil within him, caused him to bring about the Fall of Man.