Captain was a military, naval or police rank.
Known Captains
Time Lord
The Chancellery Guard had Captains among its ranks. They ranked below the Castellan and directly below the Commanders. (AUDIO: Gallifrey)
Janartis was a captain in the Chancellery Guard, later promoted to Commander, who sided with Imperiatrix Pandora during her attempt to take over Gallifrey. (AUDIO: Warfare)
Henzil was one of the Captains in Lord President Romana II's efforts against Pandora in the Gallifreyan Civil War. (AUDIO: Fractures)
Solex was a captain in the Chancellery Guard. (AUDIO: Legion of the Lost)
The Eleventh Doctor considered himself the captain of his TARDIS. (COMIC: Assimilation²)
Human
Henry Avery was Captain of the Fancy. (TV: The Smugglers, The Curse of the Black Spot)
James Cook was the captain of the Endeavour in 1770. (AUDIO: The Transit of Venus)
Bates was a British Royal Marines Captain. (TV: The Curse of Fenric)
Brookes, (PROSE: The Burning) Ransom, (TV: The War Games) Brent (PROSE: Time and Relative) and Harker (TV: The Claws of Axos) were Captains of the British Army.
Britt was a Confederate captain during the American Civil War. (AUDIO: The Runaway Train)
Chin Lee was a Captain of the Chinese Army. (TV: The Mind of Evil)
Cook was an intergalactic explorer who called himself Captain. (TV: The Greatest Show in the Galaxy)
Dent was a Captain of the IMC. (TV: Colony in Space)
Both Jack Harkness (TV: The Empty Child) and John Hart (TV: Kiss Kiss, Bang Bang) had the rank of Captain as part of their assumed aliases.
John Hart was a Captain of the Royal Navy. (TV: The Sea Devils)
Hopper was Captain of Professor Parry's expedition to Telos. (TV: The Tomb of the Cybermen)
Jabel was the captain of the Tesh. (TV: The Face of Evil)
Ben Knight was a Captain in 1 PARA under Colonel Pemberton. (TV: The Web of Fear)
Maitland was Captain of an Earth ship that discovered the Sense Sphere. (TV: The Sensorites)
Samuel Pike was a pirate captain of the Black Albatross. (TV: The Smugglers)
Revere was the leader of the human colony on Frontios. (TV: Frontios)
Rigg was the commanding Captain of the Empress. (TV: Nightmare of Eden)
Rossini was the Captain of the guard of San Martino in 1492. (TV: The Masque of Mandragora)
Sorin was the leader of a Red Army commando unit who arrived at Maiden's Point, by way of Northumberland, in 1943. (TV: The Curse of Fenric)
Captains Stapley and Urquhart were the pilots of the Concorde designated Golf Alpha Charlie in 1982. (TV: Time-Flight)
Walker was the captain of the Sanctuary Base 6 crew. (WC: Tardisode 8)
Kaido was the captain of a troop of human soldiers. (COMIC: The Child of Time)
Harvey, (PROSE: Invaders Invisible) Jimmy Turner, (TV: The Invasion) Mike Yates, (TV: Terror of the Autons) Sam Hawkins, (TV: Doctor Who and the Silurians) James Munro, (TV: Spearhead from Space) Marion Price, (TV: The Sontaran Stratagem/The Poison Sky) Erisa Magambo (TV: Turn Left) and Josh Carter (AUDIO: Armageddon) were UNIT Captains.
Vay was also a Captain. (PROSE: The Dalek Factor)
In a parallel universe, James T. Kirk was captain of the USS Enterprise (NCC-1701) in the 23rd century. In the 24th century, Jean-Luc Picard was captain of the USS Enterprise (NCC-1701-D). (COMIC: Assimilation²)
Other
Edal was the captain of the guards in the city of the Elders. (TV: The Savages)
Hardaker was Captain of the space cruise liner Titanic, operated by Max Capricorn Cruiseliners. (TV: Voyage of the Damned)
Captains Striker and Wrack were Eternals who participated in the race for Enlightenment. (TV: Enlightenment)
Vengorr was a Captain who worked with Sub-Technician Thon. (AUDIO: Living Legend)
Unnamed captains
The Captain was a space pirate who ruled the planet Zanak. (TV: The Pirate Planet)
An Alien Space Captain was in charge of the attempt by a group of radioactive aliens to make peaceful contact with Earth. (TV: The Ambassadors of Death)
An Atlantean captain was the leader of a space mission sent by the Supreme Council of Atlantis. (PROSE: The Lost Ones)
An Aztec captain guarded the place where Ian and Susan were held for punishment. (TV: The Aztecs)
A Captain of the SS Bernice ordered a search for the Third Doctor and Jo Grant because of their unauthorised presence on his ship. (TV: Carnival of Monsters)
There was a Captain of the passenger rocket that was overun by Ice Warriors. (AUDIO: Deimos/The Resurrection of Mars)
The Captain of the Guard was part of the Guard of Florence. (TV: The Massacre)
A Captain was the officer in charge of the army detachment summoned by Sir Charles Summer to investigate the warehouse in Covent Garden where the first War Machine was being constructed in July 1966. (TV: The War Machines)
A Draconian captain boarded the Master's spaceship when it violated Draconian space. A Earth cruiser captain was the ranking officer of Earth Empire battle cruiser X-29. (TV: Frontier in Space)
One Guard Captain was the head of the citadel guards on Peladon. (TV: The Curse of Peladon) Another Guard Captain was also head of the citadel guards. (TV: The Monster of Peladon)
A Shrieve captain was the commander of the Shrieves guarding the crown jewels of Ribos, housed in the relic-room of the city of Shur. (TV: The Ribos Operation)
A Space Captain received the distress signal from the crashed UK-201 on Dido and proceeded there to rescue Vicki and Bennett. (TV: The Rescue)
The Judoon had various captains. (TV: Smith and Jones, The Stolen Earth, The Pandorica Opens, Prisoner of the Judoon, COMIC: The Forgotten)
There were also three other unnamed Captains: Guard Captain, (TV: The Enemy of the World) Guard Captain (TV: Planet of the Spiders) and Captain. (AUDIO: The Wreck of the Titan)
Fictional captains
Captain Jack Harkaway was a fictional character whose adventures appeared in The Ensign, a boys' magazine. (TV: The Mind Robber)
Captain Millennium was a television series that aired on the planet Olleril. (PROSE: Tragedy Day)
Captain Scarlet was a fictional character from the TV series of the same name who could not die. (AUDIO: The Dead Line, TV: Children of Earth)
Equivalents
Platform One had no captain, instead it had a steward and his staff. (TV: The End of the World)