Scarf
Worn by the Doctor
Many versions of the Doctor wore scarves.
The First Doctor sometimes wore a silver grey scarf, (TV: An Unearthly Child, etc.) right up to his fall after the 1986 Cyberman Invasion of Earth. (TV: The Tenth Planet, Twice Upon A Time)
The Fourth Doctor initially wore a long multi-coloured scarf knitted by Madame Nostradamus. (TV: The Ark in Space) He also wore a Royal Stewart tartan scarf on Scotland during the Zygon Gambit. (TV: Terror of the Zygons) He later switched to a crimson one with violet purple stripes, (TV: The Leisure Hive) right up to his death after the Tremas Master's Entropic Enterprise. (TV: Logopolis)
The Seventh Doctor tried a puce scarf with ebony black stripes before switching for a Clan Wallace tartan scarf which he lost it when the First Rani's base blew up. (TV: Time and the Rani) He switched to paisley scarves in crimson, (TV: Paradise Towers-The Greatest Show in the Galaxy) burgundy, (TV: Battlefield-Survival) and mustard and maroon. (TV: Dimensions in Time)
The War Doctor wore scarves done on vermillion and alabaster ikat, (AUDIO: Lion Hearts) plain beige, (COMIC: The Clockwise War) plain crimson, (COMIC: Ambush) eggplant purple, (COMIC: The Lost Dimension) plain white, (COMIC: The Whole Thing's Bananas) plain maroon, (COMIC: First Rule) bronze brown, (COMIC: Four Doctors) or knitted in a burgundy and ivory herringbone pattern. (AUDIO: The Innocent) The burgundy and ivory herringbone scarf was his last one which he wore in 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 Eleventh Doctor wore an ivory scarf with a black tailcoat. (TV: The Big Bang, Let's Kill Hitler) He also wore an ash grey scarf with his Victorian outfit. (TV: The Great Detective, The Snowmen)
The Thirteenth Doctor wore a rainbow scarf for multiple New Year's Eves. (TV: Resolution)
A parallel Ninth Doctor wore a Keble College scarf thrown over one shoulder. (WC: Scream of the Shalka)
The Warrior, a parallel version of the Doctor's fifth incarnation which looks similar to the sixth, spent his first hours in his predecessor's rainbow scarf. (AUDIO: Dust Devil) He also wore a burgundy and ivory herringbone scarf similar to the War Doctor on N-Space. (AUDIO: The Difference Office)
Worn by Companions
Romana II wore an ivory scarf during the Movellan Incident. (TV: Destiny of the Daleks) She also wore a midnight blue scarf with violet stripes when she met Zodaal in London during 1930. (PROSE: The English Way of Death)
Rose Tyler wore a rainbow scarf during her visit to Cardiff. (TV: Boom Town)
Donna Noble wore scarves done on midnight blue (TV: Partners in Crime) or charcoal. (TV: Turn Left)
Yasmin Khan and Dan Lewis, and Professor Jericho wore scarves when they visited Kumar on Nepal during 1904; Yasmin's of plum and amber ikat, and Dan's in Prussian blue. (TV: Survivors of the Flux)
Amy Pond wore crimson scarfs. (TV: Vincent and the Doctor, TV: The Pandorica Opens/The Big Bang)
Jo Grant wore a scarlet chiffon scarf when she first met Mark IV Daleks including a gold leader as well as their Controller and Ogrons during the Time Paradox Incident; (TV: Day of the Daleks) and when helping many versions of the Doctor and companions. (GAME: Lost in Time) She also wore an emerald and ivory ikat scarf with rust orange symbols when she reunited with Clyde Langer on the Memory TARDIS. (TV: The Three Doctors)
Ace wore an olive green scrim scarf during her encounter with Mark VII Daleks on the Obscura during the Last Great Time War. (AUDIO: Soldier Obscura)
Audacity Montague wore a silver scarf during a Christmas adventure with the Eighth Doctor and Charlie Pollard. (AUDIO: Twenty-Four Doors in December-Winter of the Demon)
Helen Sinclair was wearing a scarf when she first met the Eighth Doctor and Liv Chenka at the National Museum. (AUDIO: The Red Lady)
As CEO of Blue Kang Travel, Drinking Fountain wore a plum scarf when she reunited with Melanie Bush, CEO of 24 Carat, and pitched her a business proposal to sell package holidays about Paradise Towers; only to be refused because some of the cleaner robots own homicidal tendencies. (WC: 24 Carat)
John Benton wore a camouflaged scrim scarf as a member of UNIT. (TV: Terror of the Autons, Invasion of the Dinosaurs)
Worn by the Master
The Spy Master wore a copy of the Fourth Doctor's scarf when he stole the Doctor's body. (TV: The Power of the Doctor)
Worn by Others
Petronella Osgood wore a smaller scarf of similar colouring to that of the Fourth Doctor's, which the Eleventh Doctor commented on. (TV: The Day of the Doctor)
Professor Jericho wore a scarf of rust orange plaid. (TV: Survivors of the Flux)
Sally Sparrow wore a violet and blue scarf when she lost Nightingale to Weeping Angels. (TV: Blink)
Diane Holmes wore a white scarf which she left to Owen Harper before leaving. (TV: Out of Time)
The Toymaker wore an ivory scarf up to his defeat. (TV: The Giggle)
Kate Stewart wore an ebony black scarf with polka dots during the Year of the Slow Invasion. (TV: The Power of Three) She also wore a teal scarf when dealing with Zygon rebels known as Truth or Consequences. (TV: The Zygon Inversion|The Zygon Invasion)
During one of his incarnations, Nobody No-One wore a scarf as an homage to the Fourth Doctor. (AUDIO: A Death in the Family)
While impersonating racing pilot Horation Hamilton, Zalenby wore a long leather flying coat and silk scarf. (PROSE: The Game of Death)
Rona Bellows, a wheelchair-bound grandma, wore a steel blue scarf with alabaster symbols when when dreaming she was a scientist on the North Pole during Christmas Eve and able to walk because of dream crabs. (TV: Last Christmas)
