Tie

A tie is an article of clothing commonly associated with men's apparel on the planet Earth. It is also favored by the Doctor in most of his incarnations. A tie consists of a piece of cloth (most commonly silk, but commonly also polyester, wool, cotton, or other fabrics) wrapped around the collar of the wearer's shirt and often folded under it. A bow tie is, as the name would suggest, tied in a bow, whereas a four-in-hand tie is longer and straighter, and tied either in the eponymous four-in-hand knot or another alternative, such as the Windsor, of half-Windsor knot. A cravat is usually not so much tied as folded, and worn under a vest with more formal attire. Ties can be worm for their style value, but can also signal levels of formality, or association with schools, companies, or other groups.

Doctors
The First Doctor 

The First Doctor almost always wears a wing collar with a bow tie which takes the form of a long, oblong piece of cloth tied in a large bow. It is almost always dark in color, but in DW: The Rescue, he wore a tie that was had a loud, black-and-white checked pattern.

The Second Doctor 

The Second Doctor typically wears a small, pre-tied bow tie. He attaches it to his shirt with a safety pin, and it also performs the function of closing the top of his shirt, in place of a collar button.

The Third Doctor 

The Third Doctor occasionally wears ties, favoring large velvet butterfly-style bow ties to go with his distinctive velvet smoking jackets.

The Fourth Doctor 

The Fourth Doctor sometimes wears a four-in-hand tie, but also often goes tieless or wears a loose cravat or neckscarf.

The Fifth Doctor 

The Fifth Doctor is not seen to wear ties, in keeping with the sporting nature of the cricket-appropriate clothes he usually wears.

The Sixth Doctor 

The Sixth Doctor wears long bow ties in a loose knot in the style of the First Doctor, but his become wider at the ends with diagonal edges. Additionally, rather than being plain they are either bright blue or red with polka dots, or yellow with a starfield pattern.

The Seventh Doctor 

The Seventh Doctor usually wears a four-in-hand tie in a paisley pattern.

The Eighth Doctor 

The Eighth Doctor typically adopts a silky cravat, originating with the Wild Bill Hickok costume that he appropriated shortly after regeneration.

The Ninth Doctor 

The Ninth Doctor does not wear ties on screen, in keeping with his general apathy to clothes relative to his other incarnations.

The Tenth Doctor 

The Tenth Doctor usually wears four-in-hand ties of various patterns with his suits, but he also goes open-collared sometimes, and wears a bow tie when dressed for formal occasions in DW: The Lazarus Experiment and DW: Voyage of the Damned.

The Eleventh Doctor 

The Eleventh Doctor wears pre-tied red and blue bow ties, frequently remarking on how he considers them to be "cool."

Other Characters
Ian Chesterton often wears a four-in-hand tie while travelling with the Doctor. He may see this level of formality as appropriate since he is still a teacher travelling with his student, Susan.

Vislor Turlough continues to wear his Brendon Public School uniform, complete with school tie and wing collar, through most of his travels with the Doctor.