From ancient times Hermes's winged caduceus has been the symbol of doctors.
The reason is that the serpent was the sacred animal of the god of medicine, Asklepios, and therefore he has traditionally been portrayed with a caduceus.
Worship of serpents was widespread in Antiquity. In Greece it was believed that dead heroes lived on the shape of serpents and might be a sort of messenger between the deceased in the underworld and living creatures.