Hermaphroditos

Hellenistic statue of Hermaphroditos, marble copy of a fresco from Herculaneum, via Wikimedia Commons

Hermaphroditos was the offspring of Hermes and Aphrodite, so much everyone seem to agree on. My knowledge in classical greek is more or less non existent but s/he seem to have a bit of a mixed bunch of lore surrounding hem. Hermes was the son of Zeus and Maia (the daughter of Atlas). 
First of all, s/he's usually referred to as a 'he'... maybe because s/he's seen as an effeminate male.
He was originally a male Aphrodite called Aphroditus but later became a compound being. According to Ovid, this happened when a nymph fell in unreciprocated love with his beauty and pleaded with the gods to unite with him forever. Hermaphroditus, apparently, wasn't too happy. 
S/he had hir place among the winged Erotes and was the god of hermaphrodites and effeminate men. The common deptictions shows a woman's body, including feminine hairstyle, but with male genitalia.
Sources:
Greek Mythology Index Theoi Greek Mythology

Hermaphroditos and Silenus, Pompei. By Stefano Bolognini (Own work) [Attribution], via Wikimedia Commons