Pirates were criminals who robbed ships at sea (or, in the case of space pirates, ships in space).
The First Doctor sailed around the Caribbean on a pirate galleon. (PDA: Byzantium!)
Samuel Pike was a pirate captain in the 17th century who searched for the treasure of pirate captain Avery. (DW: The Smugglers)
In the 17th century the Eleventh Doctor encountered the pirate ship the Fancy led by Captain Henry Avery. (DW: The Curse of the Black Spot)
Jack Lawrence was a pirate captain in the 17th century who met his end in a battle with Daleks. (DWBIT: #19)
Red Jasper was a pirate captain in the 18th century who encountered the Sixth Doctor and Evelyn Smythe. (BFA: Doctor Who and the Pirates)
Blackbeard was a pirate captain in the 18th century and the subject of several works of fiction. (DW: The Mind Robber)
Before 2050, Huskian pirates took the Ukkan library card containing the planet Urlic from the Ukkan archives. (K9TV: Lost Library of Ukko)
Kaliko was a pirate captain in the 40th century who robbed the Oil Corp Oil Rigs on Boukon. (DW: 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. (DW: Enlightenment)
Nathan li Shao was a sky pirate in a pocket universe created by a Charon. (NA: Sky Pirates!)
Quarsian pirates attempted to steal the diamonds of Sartor, but were defeated by the Tenth Doctor. (DWBIT: The Diamonds of Sartor / Quarsian Mission / Android of Death)