Penguins were birds that lived in cold or wet places. They mostly gathered in polar regions. Antarctica was often associated to penguins due to their presence on the continent. (PROSE: EarthWorld)
Penguins mated for life and often appeared on greetings cards. (TV: Something Borrowed)
History
In 1970s London, the Third Doctor and the Brigadier encountered penguins at a zoo. They had dived into their pool to escape a flock of parrots which were attacking them, but the penguins attacked them as well. (COMIC: The Arkwood Experiments)
In 2048, Patricia Audley had a pet penguin, which she named "Poopsie". (COMIC: Blood and Ice)
In 7214, specimen of penguins were held in a nature preserve in Antarctopolis, Antarctica having been urbanised. (COMIC: Facades)
References
One of the TV shows Cal watched in her dream world was about penguins. (TV: Silence in the Library)
The Tenth Doctor insisted that the North Pole did not have penguins, contrary to popular belief. (PROSE: The Frozen Wastes)
Bill described the Twelfth Doctor's running as "a penguin with its arse on fire". (TV: The Pilot, Smile)
Frobisher
Frobisher took on the form of a penguin as his wife Francine had been fond of them. He occasionally changed between variations of the species. (COMIC: Voyager)
Alternate timelines
In an alternate timeline, penguins lived on the River Nile in Egypt. (TV: The Big Bang)