She’s often depicted holding torches, keys, scourge, knife, or some combination thereof. Sometimes she’s wearing a polos (headdress) or described as wearing a single sandal.
The keys could be symbols of knowledge, such as keys to the secrets of the Universe. The Orhpic hymn to Hekate addresses her as “holder of the keys of Cosmos”. They could also be keys that open the gates to the Underworld, or actual keys to a temple. The keys played some role in Hekate’s cult, but we don’t know much about it. Strabo tells of a “procession of the key” held each year in Asia Minor (and if the lovely people at The Perseus Project ever get the databases working again I’ll provide the passage. If you want to look it up for yourself, it’s Strabo’s Geography XIV 25).
The scourge she probably borrowed from the Erinyes, underwordly deities who punished mortals who broke oaths or killed members of their own family.
Neo-Pagan web sites typically claim that the knife is a symbol of Hekate’s role as midwife, and that it’s used for cutting the umbilical cord. It could just as well be a sacrifical knife, or a knife for cutting herbs. Nobody knows.
The single sandal is golden, bronze, or brazen. In Porphyry’s On Images Hekate’s symbols very with the phases of the moon.
But, again, the moon is Hecate, the symbol of her varying phases and of her power dependent on the phases. Wherefore her power appears in three forms, having as symbol of the new moon the figure in the white robe and golden sandals, and torches lighted: the basket, which she bears when she has mounted high, is the symbol of the cultivation of the crops, which she makes to grow up according to the increase of her light: and again the symbol of the full moon is the goddess of the brazen sandals.