At least two living sphinxes were known.
Jason and the Argonauts encountered a sphinx from Satroz when an alien prison ship crashed on Earth. She was shot dead by the Parthenope prisoners. (PROSE: Island of the Sirens) In the mists of Gallifreyan history, the Pythia went to the island of Thule to steal the eye of its resident sphinx so that she could put it in place of her own eye that she had gouged out. (PROSE: Cat's Cradle: Time's Crucible)
Sphinxes, though, were perhaps better known not as living entities, but as the subjects of artistic renderings — typically very large statues. The two most famous sphinx statues were undoubtedly the Great Sphinx in Giza, Egypt and the Martian Sphinx.
However, there was also one at the New Jupiter EarthWorld theme park — even though it confused Egyptian and Greek legends. The riddle of the sphinx, "What walks on four legs in the morning, two legs in the afternoon, and three legs by nightfall?" came from Greek legends. The answer was "man". The Egyptian Zone's sphinx asked this question to anyone trying to enter the pyramid. Anji Kapoor gave the answer before it was asked because she was trying to outrun robotic dinosaurs. The huge sphinx also had wings like an eagle and a missing nose like the Great Sphinx. (PROSE: EarthWorld)