Pirates were criminals who robbed ships at sea. Space pirates did the same to vessels in space.
The First Doctor sailed around the Caribbean on a pirate galleon. (PROSE: Byzantium!)
Achilles called Odysseus a pirate. (TV: The Myth Makers)
In 1588, the Fourth Doctor referred to Sir Francis Drake as a pirate. (AUDIO: The Devil's Armada)
Samuel Pike was a pirate captain in the 17th century who searched for the treasure of pirate captain Avery. (TV: The Smugglers)
Also in the 17th century, the Eleventh Doctor, along with Amy Pond and Rory Williams, then encountered Captain Henry Avery himself on his pirate ship the Fancy, before he disappeared. (TV: The Curse of the Black Spot)
Red Jasper was a pirate captain in the 18th century who encountered the Sixth Doctor and Evelyn Smythe. (AUDIO: Doctor Who and the Pirates)
Blackbeard was a pirate captain in the 18th century and the subject of several works of fiction. (TV: The Mind Robber)
Before 2050, Huskian pirates took the Ukkan library card containing the planet Urlic from the Ukkan archives. (TV: Lost Library of Ukko)
Kaliko was a pirate captain in the 40th century who robbed the Oil Corp Oil Rigs on Boukon. (TV: The Infinite Quest)
In the race for Enlightenment, Wrack's ship, the Buccaneer, resembled a pirate ship. The crew were all pirates who had been taken from their time-period. (TV: Enlightenment)
Nathan li Shao was a sky pirate in a pocket universe created by a Charon. (PROSE: Sky Pirates!)
Pym was the captain of the pirate ship Parliament of Rats on the planet Lethe. (PROSE: The Parliament of Rats)
Quarsian pirates attempted to steal the diamonds of Sartor, but were defeated by the Tenth Doctor. (COMIC: The Diamonds of Sartor / Quarsian Mission / Android of Death)
The First Doctor encountered pirates on an unnamed planet who were capable of breathing underwater. (PROSE: Ten Fathom Pirates)
Pyras was a planet home to robots resembling pirates that were controlled by sentient parrots. (PROSE: Battleship Anathema)
Behind the scenes
According to non-narrative information in DWBIT 19, Jack Lawrence was a pirate captain in the 17th century who met his end in a battle with Daleks.
Philip Morris, discoverer of missing episodes of The Enemy of the World and The Web of Fear, was kidnapped by pirates and then suffered from PTSD.