The Doctor's scarf

The Doctor's scarf was a long, multicoloured piece of knitwear that was an important part of the Doctor's outfit during his fourth incarnation. At least two such scarves existed. (DW: Robot, Leisure Hive)

When the Doctor, shortly after his third regeneration, had to accompany the Brigadier on a journey, he tried on several inappropriate costumes before settling on a vaguely bohemian outfit, which included a wide brimmed hat and a long scarf. (DW: Robot) The scarf had originally been made for the Doctor by Madame Nostradamus. (DW: The Ark in Space)

Romana II donned a similar outfit, including a scarf, shortly after her regeneration. (DW: Destiny of the Daleks)

The Doctor once mentioned that, had he not produced a ball of string for Theseus and Ariadne, they would have unravelled his scarf to escape the labyrinth. (DW: The Creature from the Pit)

Later in this incarnation, the Doctor switched to a scarf of similar length, but coloured in shades of burgundy. (DW: Leisure Hive) However, his original scarf was seen to be kept on a hatstand in the console room. (DW: Warriors' Gate)

After his fourth regeneration, the Fifth Doctor unravelled his burgundy scarf in the TARDIS corridors, allowing his companions to follow him. (DW: Castrovalva)

The Fifth Doctor admitted that the scarf was warm and useful in situations, though he did trip on it occasionally. (BFA: No Place Like Home)

While selecting an outfit following his seventh regeneration, the Doctor discovered a similar multi-coloured scarf in a hospital locker. He did not include it in his outfit. (DW: Doctor Who)

The Ninth Doctor supossedly sold one of his scarves, as Dinah May posted in whoisdoctorwho:

'':I saw this man several years ago, dumping some old clothes at the local tip. There was a flute, a velvet jacket and a long scarf. I asked him about them, and he just said he was having a clear out. Then he said he had never really liked cricket either. ''

The TARDIS wardrobe was seen to contain a multi-colour scarf during the Doctor's tenth incarnation. (DW: The Christmas Invasion)

The Eleventh Doctor and Kazran Sardick were both seen to wear scarves similar to the Fourth Doctor's during their earlier adventures when visiting Abigail Pettigrew. (DW: A Christmas Carol)

The scarf eventually ended up in the Doctor's study onboard the TARDIS. (VG: TARDIS)

Uses
The scarf proved to be useful, on many occasions, as something other than a piece of attire.


 * On the Nerva station, the Doctor unsuccessfully used it to try to deactivate the Auto guard. (DW: The Ark in Space)
 * It was used to measure a puzzle. (DW: Pyramids of Mars)
 * Escaping from Count Federico's executioner (DW: The Masque of Mandragora)
 * Tripping Eldrad down a chasm. (DW: The Hand of Fear)
 * In the Matrix on Gallifrey to prevent the Doctor from falling down a cliff face. (DW: The Deadly Assassin)
 * As a lead to drag K9 about when his power had run down. (DW: The Invisible Enemy)
 * Climbing a mine shaft using the scarf as a rope (DW: The Creature from the Pit)

Behind the scenes

 * When asked to knit a scarf for the new Doctor, Begonia Pope was unsure how long a scarf was required. She consequently used all of the wool she had been given, resulting in a ridiculously long scarf. The producers loved it and, after it had been shortened slightly, used it for the Fourth Doctor's first story.
 * There were many scarves used during the Tom Baker era, including a much shorter "stunt scarf" for action sequences. The pattern and coloration varied from season to season, as did the overall length of the scarf, which, at one point reached a maximum length of 24ft (nearly four times the height of Tom Baker himself!).
 * When June Hudson was asked to design a new outfit for the Doctor at the start of Season 18, she was given the option to omit the scarf by John Nathan-Turner. In the end, she decided the scarf had become too much a part of the Doctor's image to omit, and designed a new scarf to go along with the new Burgundy colour scheme of the Doctor's outfit.
 * In VG: TARDIS, the Fourth Doctor's scarf can be seen in the drawing room.