Tibetan Yeti

Tibetan Yeti, also known as Abominable Snowmen, were anthropoid creatures that dwelt in the Tibetan Himalayas on Earth.

History
Little was known about them, except that they were large, furry, probably semi-sapient humanoids. They were timid, rarely approaching travellers and most in the western world considered them myths.

Professor Travers went on an expedition to find them in 1935 in order to prove that they actually existed. After an adventure with the Second Doctor and the Robot Yeti, Travers spotted one and went off in pursuit. (DW: The Abominable Snowmen) He was unable to catch up with the creature, though, and several years later appeared not be in possession of any evidence of the species' existence. (DW: The Web of Fear)

Decades later, a team of monster hunters attempted to photograph the elusive Yeti and were captured by the Great Intelligence responsible for the creation of the Robot Yeti. Lama Gampo, a monk who had sworn to protect the world from the Intelligence, blew a great horn and called the real Yeti, who howled in response and descended the mountains to fight against their robotic counterparts. (DWM: Yonder... The Yeti)

Possible Sightings
According to Bea Nelson-Stanley, the Sultan of Ishkanbar had seen a Yeti. (SJA: Eye of the Gorgon)

The Museum of Things That Don't Exist had nine different varieties of Yeti that all supposedly didn't exist. However, the exhibits weren't known for their accuracy. (EDA: The Taking of Planet 5)

Behind the scenes

 * The question of whether there are "real" Yetis in the Whoniverse is not possible to definitively answer just from televised episodes alone, although it appears to have been implied as indicated below.
 * One may have appeared at the end of The Abominable Snowmen, but the script is considerably unclear as to this point. According to production records of the now-wiped serial, the supposed "real" Yeti would only have been briefly glimpsed in a long shot, and it may have been depicted with a slightly "slimmed-down" version of the robot Yeti costumes. Whether that would have been enough for viewers to actually detect a difference between the "real" and robotic Yeti is unknown. Certainly, production records indicate that a close-up of a "real" Yeti has never been shot for televised Doctor Who.
 * The Target Books novelisations Doctor Who and the Abominable Snowmen and Doctor Who and the Web of Fear definitiely refer to "real" Yetis in ways that the televised episodes don't. The Snowmen novelisation gives a vivid depiction of the difference between living and robotic Yetis, but this description is at variance with what viewers would have been able to detect in a monochromatic long shot on television. And, despite the fact that Travers recalls the "real" Yeti in the novelisation, the Fear script never mentions "real" Yeti whatsoever. It even makes it possible for viewers to assume that the robot Yeti he returned to London was in fact the "real" Yeti he'd been chasing at the end of Abominable.
 * A possible image of the "real" Yeti of Abominable does exist. However, as it's a telesnap, and all location work for the serial was done in a mere six days, it's entirely possible this image didn't come from episode six at all. There's a sequence in episode four where a lone robotic Yeti climbs a mountain, and the surviving telesnap could in fact have documented that sequence, instead. Or it could be an outtake of a Yeti-portrayer falling down the mountain, since it is known that the Yeti-portrayers were constantly slipping on muddy patches during the shoot. Even if it is real, the shot in no way clearly distinguishes its subject from a robotic Yeti.
 * As of 2010, the clearest surviving documentation of "real" Yetis is the Doctor Who Magazine comic strip, Yonder... The Yeti.