The scarf has had such a big role in Doctor Who, it should be listed in the opening credits! Here are just a few scarf-y star turns. Make sure to check out The Doctor Who Wiki's entry about "The Doctor's scarf" for a great, thorough collection of the scarf's star moments! Also take a good look at Doctor Who Scarf, a fantastic resource for any fan who wants to create a Who scarf for themselves!
Series 12: Robot
Using his scarf as a makeshift tape measure, the Fourth Doctor measures a large hole and quips: "It seems you have a very large rat, Brigadier - maybe you should employ the services of a very large cat?"
Series 12: The Ark in Space
The Fourth Doctor flings the scarf to trigger a switch, but the scarf gets zapped and singed in the process! Lamenting the damage, he reveals the scarf's origins: "Pity about the scarf. Madame Nostradamus made it for me. A witty little knitter..."
Series 16: The Androids of Tara
Threatened with death by a zap-happy guard, the Fourth Doctor stands up for his scarf: "If you keep burning my scarf, you're going to have to kill me!"
Series 18: The Leisure Hive
The Fourth Doctor is accused of murder! A character notes that the scarf was the murder weapon. "Arrest the scarf, then," the Doctor reasons.
New Who, The Day of the Doctor (2013 Special)
The Eleventh Doctor appreciates UNIT scientist Osgood's taste in familiarly striped, lengthy knitwear: "Nice scarf."
New Who, Series 8: Deep Breath
The newly regenerated Twelfth Doctor has changed his mind about the scarf! "I need clothes, that's what I need. And a big, long scarf. No, I've moved on from that. Looks stupid."
New Who, Series 8: Time Heist
The Twelfth Doctor dubs some of his past looks - including the "big scarf" - "a bit embarrassing." Say it ain't so, Doc!