A cravat was a form of clothing worn around the neck.
Worn by the Doctor
The Third Doctor wore a number of cravats throughout his life. Immediately following his regeneration, he adopted a black cravat, which he wore for a notable period. (TV: Spearhead from Space - Inferno) He then became sporadic in his adoption of cravats, wearing his original whilst combatting the Sea Devils (TV: The Sea Devils) and during his visit inside a miniscope, (TV: Carnival of Monsters) and adopting new patterned ones on a number of occasions. (TV: The Dæmons, The Mutants, Carnival of Monsters)
The Fourth Doctor wore cravats for a period, initially adopting ones green, (TV: Terror of the Zygons) blue and terracotta in colour, (TV: Planet of Evil, Pyramids of Mars) before settling on a maroon one. (TV: The Android Invasion - The Robots of Death) He also wore a cravat of ivory dupioni. (TV: The Invasion of Time - The Pirate Planet)
The Sixth Doctor wore a wide variety of cravats, them being a mainstay of his outfit. His first cravat was turquoise with a polka dot pattern, (TV: The Twin Dilemma) which he eventually replaced with a similar cravat in red. (TV: The Mysterious Planet) During his travels with Evelyn Smythe, he briefly returned to wearing a turquoise cravat, this time without polka dots, (WC: Real Time) but soon returned to wearing cravats with such a pattern. After briefly wearing yet another polka dot cravat, this time in purple, (PROSE: The Quantum Archangel) he adopted a yellow cravat with a starfield design. (TV: Terror of the Vervoids) By the time of his regeneration, he had returned to wearing his red cravat. (TV: Time and the Rani)
The Seventh Doctor wore a black cravat with his dark jacket. (PROSE: St Anthony's Fire) During his escapades as Time's Champion, he wore a green silk cravat. (PROSE: White Darkness)
The Eighth Doctor often wore a dupioni cravat, first adopting a battleship grey cravat shortly after his regeneration. (TV: Doctor Who) He also wore some in indigo, (COMIC: Dreadnought) plum purple, (COMIC: Descendance) amber, (COMIC: Ophidius) gold, (AUDIO: The Stones of Venice) and emerald. (AUDIO: Caerdroia)
The Ninth Doctor wore a burgundy brocade cravat in 1912 Southampton, (TV: Rose)
The Eleventh Doctor wore a black cravat on Victorian London. (TV: The Snowmen)
Sometimes, the Twelfth Doctor sometines wore a black cravat. (TV: Mummy on the Orient Express, Thin Ice)
Worn by Companions
Leela wore a scarlet cravat with her walking suit when she and the Fourth Doctor went to London during 1892. (TV: The Talons of Weng-Chiang)
Jenny Flint wore cravats with her waistcoats and her shirts. (TV: A Good Man Goes to War, Deep Breath; PROSE: The Dangerous Dilemma of the Dream Doorway)
Bill Potts wore an ivory cravat during her trip to the 1814 frost fair. (TV: Thin Ice)
Yasmin Khan wore a cravat of bronze tartan. (TV: Survivors of the Flux, The Vanquishers)
Josie Day wore cravats done on jade (COMIC: A Matter of Life and Death) and indigo (COMIC: The Lost Dimension)
Amy Pond wore a black and white cheque cravat with her policewoman outfit. (TV: The Eleventh Hour)
Worn by the Master
Many incarnations of the Master wore cravats.
John Smith, a human persona of the Decayed Master, wore a black cravat. (AUDIO: Master)
When he was posing as the 'Other Doctor', the Bald Master wore cravats done in emerald green or gold. (AUDIO: Dominion)
During the Last Great Time War, the War Master wore black cravats; (AUDIO: Only the Good, The Master of Callous, Rage of the Time Lords, Day of the Master, etc.) including one in basic form when he was Professor Yana. (TV: Utopia)
Missy, his gender-switched incarnation, wore a rust orange cravat. (TV: Extremis-The Doctor Falls)
The Spy Master wore a black cravat when he met the Thirteenth Doctor on London during 1834. (TV: Spyfall)
Won by Others
Emily Morris, the 19th century girl who helped Sarah Jane, wore an ivory cravat with black spots. (TV: Lost in Time)
Jackson Lake wore a gold cravat when he and Rosita worked with the Tenth Doctor to stop Cybermen from Pete's World. (TV: The Next Doctor)
George Litefoot wore black cravats. (TV: The Talons of Weng-Chiang; AUDIO: Voyage to Venus)
Josiah wore a silver cravat with his Victorian outfit. (TV: Ghost Light)
Theodore Maxtible wore a bronze cravat. Edward Waterfield also wore a scarlet cravat in basic bow form. (TV: The Evil of the Daleks)
Webley wore a burgundy cravat on basic bow form. (TV: Nightmare in Silver)
Sergeant Calder and his clone both wore a cravat that matched the colour of their uniforms. (TV: Resurrection of the Daleks)
Walter Simeon wore tartan cravats, (TV: The Snowmen) as did the Great Intelligence when taking his form. (TV: The Name of the Doctor)