The original three Gorgons (Euryale, Medusa, Stheno) were considered daughters of the sea-deities Phorcys and Ceto. According to some mythographers of antiquity they were born beautiful and transformed to their better know appearance by the wrath of Athena. Their parents are thought to represent sea monsters and the dangers of the deep.
The Gorgons were thought to have more siblings. Including Echidna (the "She Viper", also known as "Mother of All Monsters"), the Graeae ("old women", a group of crone-like witches), and Ladon (the dragon who guarded the Guarded of the Hesperides). Some accounts also list among their siblings Thoosa (a sea nymph, better known as mother to the cyclops Polyphemus), and Scylla (a sea monster, representing dangerous straits).
The granparents of the Gorgons were Pontus and Gaea, primordial deities of (respectively) the Sea and the Earth.