Burgundy was a shade of red, purple, and brown similar to the colour of wine.
The War Doctor wore a herringbone scarf done in burgundy and ivory during the Battle for the Tantalus Eye, (PROSE: Engines of War) and right up to his death after the 1562/2013 Zygon Invasion of Earth and the Fall of Gallifrey. (TV: The Day of the Doctor)
The Third Doctor wore a burgundy velvet blazer with a rolled collar when braving the Game of Rassilon. (TV: The Five Doctors)
The Fourth Doctor wore a burgundy fedora, trenchcoat and trousers; (TV: The Leisure Hive) up to his death after the Tremas Master's Entropic Enterprise. (TV: Logopolis) His successor, the Fifth Doctor, wore them before switching for an ivory Panama hat with a crimson band, a beige frock coat with scarlet trim, and trousers with brown stripes. (TV: Logopolis, Castrovalva)
The Seventh Doctor tried a copy of the Fourth Doctor's burgundy fedora and trenchcoat before eventually going for a cream Panama hat with a scarlet paisley band and a silver grey safari jacket. (TV: Time and the Rani) He also wore a scarf and tie in burgundy and navy paisley; most notably when teaming up with his other incarnations, (COMIC: The Lost Dimension) when foiling a Dalek Supreme's efforts to steal information from Kar-Charrat for a Dalek Emperor, (AUDIO: The Genocide Machine) when teaming up with UNIT and Ancelyn to stop Morgaine and the Destroyer, (TV: Battlefield) when confronting the Light and Josiah Samuel Smith in Gabriel Chase during 1883, (TV: Ghost Light) when defeating Fenric, (TV: The Curse of Fenric) when foiling the Tremas Master's Survival Stratagem, (TV: Survival) when resisting Death to save the Decayed Master inside John Smith, (TV: Master) and when reuniting with Ace in the Memory TARDIS. (TV: The Curse of Fenric) He also wore a burgundy waistcoat during a trip to Youkali. (PROSE: Return of the Living Dad)
The Ninth Doctor wore a burgundy brocade cravat in 1912 Southampton. (TV: Rose)
The Tenth Doctor wore a navy blue tie with burgundy circles in diagonal grid during his trip to Krop Tor, (TV: The Impossible Planet|The Satan Pit) and before and after dealing with the Family of Blood. (TV: Human Nature|The Family Of Blood) He also wore a burgundy herringbone tie with mauve random flora random design when he met Martha Jones during the Royal Hope Incident, (TV: Smith and Jones) during the 2009 Sontaran Invasion of Earth. (TV: The Sontaran Stratagem|The Poison Sky) and when helping the Bannerman Road Gang defy the Trickster. (TV: The Wedding Of Sarah Jane Smith) He also wore a burgundy tie with diagonal ebony black stripes before and when he met his daughter Jenny. (TV: The Poison Sky, The Doctor's Daughter)
The Eleventh Doctor's first bow tie was burgundy. He also wore a white and burgundy pinstripe shirt. (TV: The Eleventh Hour)
The Twelfth Doctor wore a burgundy dress shirt when he met Robin Hood. (TV: Robot of Sherwood) On one occasion, he wore a burgundy ladder jumper when dealing with the Harmony Shoal during the 2010s. (TV: The Return of Doctor Mysterio [+])
The Thirteenth Doctor wore a burgundy t-shirt with a crew collar during a big clash between two Dalek factions. (TV: Revolution of the Daleks)
Amy Pond wore a burgundy scarf during her visit to Venice. (TV: The Vampires of Venice)
Sarah Jane Smith wore a burgundy and grey jumper with green diamonds when she and the Third Doctor helped to save Peladon from Azaxyr and Eckersley. (TV: The Monster of Peladon)
Donna Noble wore a burgundy top during the March of the Adipose. (TV: Partners in Crime)
Yasmin Khan wore a burgundy blouse with a mandarin collar and white spots when she, the Thirteenth Doctor, and Dan helped Zheng Yi Sao and Sin Ji-Hun versus Marsissus and his followers. (TV: Legend of the Sea Devils)
Peri Brown wore a burgundy trouser suit when she met Davros and the Necros Daleks during the Necros Incident. (TV: Revelation of the Daleks)
Nyssa wore burgundy shorts during her second encounter with the Mara. (TV: Snakedance)
The War Master sometimes replaced his black cravat with a burgundy bow tie. (AUDIO: The Sincerest Form of Flattery, A Quiet Night In, The Orphan, Unfinished Business)
Webley wore a burgundy cravat on basic bow form. (TV: Nightmare in Silver)
Ian Chesterton wore a burgundy tie during a meeting of companions. (TV: The Power of the Doctor)
Petronella Osgood wore a burgundy bow tie similar to the Eleventh Doctor's. (TV: Tidal Wave)
The Toymaker wore a burgundy bow tie with ivory polka dots on Soho during 1925. (TV: The Giggle)
Captain Cook, an intergalactic explorer, wore an ascot tie of burgundy and beige paisley under the collar of his shirt. (TV: The Greatest Show in the Galaxy)
The Warrior, a parallel version of the Doctor's fifth incarnation which looks similar to the sixth, wore a burgundy and ivory herringbone scarf similar to the War Doctor on N-Space. (AUDIO: The Difference Office)
The Curator, a future version of the Doctor on N-Space, wore a burgundy ascot tie under his shirt's collar when he looked similar to the Fourth Doctor. (COMIC: The Then and the Now) In his Sixth Doctor appearance, he wore a double-breasted frock coat of burgundy moleskin with a silver sphinx cat brooch. (AUDIO: Crossed Lines)
Jo Grant wore a mauve sweater with burgundy stripes when she and the Third Doctor went to Uxarieus in 2472. (TV: Colony in Space)
John Ellis wore a burgundy tie with ivory polka dots when he landed in 21st century Cardiff. (TV: Out of Time)
Some Sontarans wore burgundy space armour with vermillion or gold helmets. (HOMEVID: Shakedown: Return of the Sontarans; PROSE: Shakedown)
The Half-Face Man wore a burgundy ascot tie during the 1890s. (TV: Deep Breath)