Mammoth

Mammoths were a species of large mammals native to Earth in Humanity's prehistory.

Around 100,000 BC, Martha Jones watched herds of mammoths while the Doctor went to retrieve the bodies of Modrikanians who had died in a crash to Earth. (NSA: Snowglobe 7)

Nimrod's Neanderthal tribe herded mammoths "sunward to find new grazing." (DW: Ghost Light) According to the the Doctor, the Neanderthals could knock up a good Mammoth casserole. (MA: The Romance of Crime)

While being pursued by the Trods through time, the Doctor visited prehistoric Earth, where he used his recorder to befriend a herd of mammoths. (TVC: Pursued by the Trods)

The Doctor and Rose on a visit to prehistoric Earth encountered a mammoth killed by a Hy-bractor. (NSA: Only Human)

After being flung back in time by a Time Cube, the Doctor, Sarah Jane, and Dr. Bhoul encounter a caveman and a raging mammoth. (DWA: The Time Snatch)

In 1774, King George III received an anachronistic mammoth as a gift from Catherine II of Russia, even though it should not have belonged in that time period. (FP: Political Animals) Most people, however regarded the story as just part of a larger tradition of strange rumours that circulated about high society, particularly about the more dubious members of the aristocracy. In 1782, during a night of drinking with the Doctor, Scarlette claimed that she had once ridden George III's mammoth.

As late as 1804, Thomas Jefferson believed that wooly mammoths still roamed North America's midwest, even sending an expedition to find one. (EDA: The Adventuress of Henrietta Street)

Alternate timelines
In an alternate timeline, the Silurians brought back the Mammoths, raising them for food and allowing them to roam the mountains of Earth. (NA: Blood Heat)

During the Second War in Heaven, Chris Cwej infiltrated the Hollywood Bowl during the filming of Mujun: The Ghost Kingdom. The introduction of a seventh main character disrupted the aesthetics of the plot enough to produce a scene where one of the character's children was taking care of George III's mammoth ten years later. (FP: The Book of the War)

Mammoth-like species

 * A zoo on an unnamed planet exhibited a mammoth or a mammoth-like creature. (TVC: The Didus Expedition
 * The Junlangis of Dellah were a white mammoth-like creatures. (BNA: Twilight of the Gods)
 * Yahoomer's species resembled orange mammoths with four trunks. (NSA: The Monsters Inside)