Hippocrates was a 5th century BC Greek physician known as the father of Earth medicine. He developed an oath of medical ethics that became known as the Hippocratic Oath and was taken by physicians until the late 24th century.
In 2152, when explaining the difference between Denobulan and Human medical ethics, Doctor Phlox stated "Hippocrates wasn't Denobulan." (ENT: "The Breach")
While the crew of the USS Enterprise visited the Platonians in 2268, Philana gave Dr. McCoy a scroll of ancient Greek cures, penned by Hippocrates himself, after McCoy saved Platonius. (TOS: "Plato's Stepchildren")
Following McCoy's release from Dramen custody, Spock chastised McCoy for being derelict in his duties, including the dispensing of the regular vitamin rations to the crew. When McCoy retorted that they both knew what he had just been through, Spock responded, "Hippocrates would not have approved of lame excuses, doctor." (TAS: "Albatross")
In 2371, when asked for some nitrogenated soil samples, The Doctor mentioned that "Now I know how Hippocrates felt when the king needed him to trim a hangnail." (VOY: "Parallax")
In 2372, while on the holodeck with Danara Pel, The Doctor explained to her who Hippocrates was. (VOY: "Lifesigns")