She's the daughter of the Titans Perses and Asteria, and is a chthonic, or Underworld, deity, having existed before the Olympians. Her grandmother is Phoebe, a personification of the moon, and through the Titaness Leto, she's cousin to the twins Apollo and Artemis.
Consorts & Children:
Hecate is said to be the mother of the minor goddess/sorceress Circe, as well as the monstrous Scylla (possibly by the primordial sea-god Phorkys) and Pasiphae (possibly by Helios), wife of King Minos.
Notable Stories Involving Her:
She has intimate knowledge of herbal lore, including poisonous plants. She is regarded with such respect that she was given some amount of dominion over the earth, the sea, and the sky. As goddess of spirits and necromancy, she's one of the few gods allowed to enter Hades's domain at will. In fact, when Hades had kidnapped Persephone, Hecate had helped Demeter to look for her by searching in the Underworld. As goddess of crossroads, she's sometimes depicted as a triple goddess, bearing twin torches, but at other times, is portrayed as a wise crone.
The dog, the weasel, and the snake are sacred to her, and her attributes include a pair of torches, a set of keys, a rope (representing an umbilical cord), and a dagger (with which to cut the umbilical cord, making her a goddess of childbirth as well).
Hecate Around the World:
The Romans knew her as Trivia, though she's also been identified with the Roman Janus, the Egyptian Heket, the Egyptian Isis, and the Celtic Cerridwen.
SOURCES: Greek Mythology.com, Encyclopedia Mythica, & Wikipedia