Unicorn

A unicorn was a mythical beast similar in appearance to a horse, but with a single long horn in the middle of its head. At least one account indicated unicorns to have actually existed. (COMIC: The Horn of a Dilemma)

History
Assassin Doom was contracted to kill the idea of the unicorn. She convinced everyone that a unicorn specimen owned by a seller was a fake with the help of Jo Grant. (COMIC: The Horn of a Dilemma)

According to George Litefoot, the Narwhal, a horned Cetacean, was thought to be the origin of the unicorn myth. (AUDIO: The Ruthven Inheritance)

In the 1890s, Henry Gordon Jago joked that London would one day be invaded by killer unicorns. (AUDIO: The Backwards Men)

The Second Doctor encountered a unicorn in the Land of Fiction. (TV: The Mind Robber)

The Ceffyl of Tír na n-Óg resembled unicorns by design. (PROSE: Cat's Cradle: Witch Mark)

In 2002, unicorns appeared in San Francisco due to a dimensional scar. (PROSE: Unnatural History)

"The Unicorn" was the alias of Ada Mullins. (TV: The Unicorn and the Wasp) After Rose-the-cat removed part of the TARDIS' wall with a chainsaw, causing great disturbances throughout all of time and space, Richard III was rescued at Ambion Hill, Leicestershire by a unicorn after he begged for a horse in 1845. (COMIC: A Rose by Any Other Name)

The Bestiary of Legendary and Magical Creatures created a unicorn out of toilet paper. (PROSE: Phoenix)

Iris Wildthyme had a unicorn statuette in her TARDIS. (PROSE: Old Flames)

The Doctor once claimed that he was a unicorn. (PROSE: Borrowed Time)

One version of David Banderson's Variations had a unicorn that didn't believe in people. The Tenth Doctor told Donna Noble that this was odd because "unicorns definitely do believe in people". (PROSE: Once Upon a Time)

The Fifth Doctor knew a version of the story of Noah's Ark in which Noah had to leave behind unicorns, centaurs, basilisks and many other such animals. (PROSE: Perfect Day)

Behind the scenes

 * Igotacat.jpg in blue. (COMIC: A Rose by Any Other Name)]]According to The Brilliant Book 2012, a book that contains non-narrative based information, in River Song's World unicorns were a pest in London, alongside Cyclops and Satyrs.
 * In COMIC: A Rose by Any Other Name, when the Tenth Doctor exclaimed "I GOT A CAT!!', among the illustrations in the panel was a unicorn coloured in blue.