Sabre-toothed tiger

According to The I-Spyder Book of Earth Creatures, the sabre-toothed tiger — formally known as Smilodon fatalis — was a species of cat native to North America that died out around 9000 BC because the global climate change killed off its prey. It had two remarkably-sized upper canine teeth, measuring up to 17 centimetres in length. It was possessed of a stout, muscular body with a thick chest, and retractable claws. It primarily ate herbivores like bison. (PROSE: The Last Dodo)

According to Dr River Song, sabre-toothed tigers, or smilodons, were not actually related to the tiger family. (AUDIO: Peepshow)

On Earth
In circa 100,000 BC, (PROSE: The Eight Doctors) the First Doctor, Susan, Barbara, and Ian were stalked by a sabre-toothed tiger, however it attacked Za instead, and was injured in the process. (TV: An Unearthly Child, PROSE: Doctor Who and an Unearthly Child) Seconds later, the Eighth Doctor, sent back in time by Rassilon shortly after his regeneration, saw the wounded sabre-tooth tiger. He surmised that it would not survive the injury. (PROSE: The Eight Doctors)

The Fourth Doctor later took a 20th century human back in time to witness a band of primitive cavemen killing a Smilodon. (PROSE: The Doctor Who Dinosaur Book)

During the Ice Age, the Eleventh Doctor and Amy Pond saved a Neanderthal from a sabre-toothed tiger. (COMIC: Snow Globe)

When the Eleventh Doctor and Rory Williams visited the future site of Los Angeles, California, a sabre-toothed tiger jumped into the TARDIS and perched on the console. Rory got it off the console by hitting it with a rolled-up magazine, and as it ran off further into the ship, the Doctor advised Rory to put it to sleep with tranquilliser-laced meat. (COMIC: The Doctor and the Nurse)

Professor Elliot Payne brought a sabre-toothed tiger to 1890s London from thousands of years in the past to act as a guard. Leela broke its neck but sustained several injuries in doing so. (AUDIO: Chronoclasm)

Crag Gorton had a sabre-toothed tiger. A soldier was prevented from shooting it by Sheik Ali Barka's servant, as later stated in a quiz by Agent Twenty One. (PROSE: )

The last sabre-toothed tiger from Earth was saved and kept in the Museum of the Last Ones. This specimen was cloned by Eve to distract people while the cloned dodos planted bombs. The sabre-toothed tiger was worth 500 points in the I-Spyder Book of Earth Creatures. Martha Jones spotted one, but only because she and the Tenth Doctor were being chased by it in England. They managed to lure it into some freshly-laid tarmac, whereupon the Doctor used the sonic screwdriver to set the asphalt and capture the tiger. (PROSE: The Last Dodo)

Alternate timelines
In an alternate timeline the sabre-toothed tiger was one of the creatures brought back from extinction by the Silurians. They were allowed to roam free and some were possibly used for hunting animals by the Silurians. (PROSE: Blood Heat)

On other worlds
Sabre-toothed tigers were also among the native species on Tiermann's World. These tigers were able to communicate complex ideas amongst themselves, and warned each other about the approaching Voracious Craw. (PROSE: Sick Building)

K9 once encountered some sabre-toothed tigers on a planet in another dimension, partially inhabited by ex-Tellac miners. They lived alongside other Earth animals from widely varying periods of evolutionary history. On this planet, he observed one fighting a mammoth. (PROSE: K9 and the Missing Planet)