Umbrella

Umbrellas offered hand-held shelter against the rain or snow. They were particularly associated with rainy climates on Earth, such as was found in the United Kingdom. The Doctor had several umbrellas over the course of his various incarnations.

Second Doctor
The Second Doctor carried an umbrella on the Gond planet because of the "twin suns. It's probably hot." Then he used it as defence against vaporisation. (TV: The Krotons)

Fourth Doctor
While visiting Derbyshire in 1979, the Fourth Doctor warned Leela that she would need an umbrella. (AUDIO: Trail of the White Worm)

The Fourth Doctor occasionally kept a multicoloured umbrella in his console room's hatstand. (TV: The Stones of Blood, Destiny of the Daleks)

Sixth Doctor
The Sixth Doctor was known to occasionally carry a bright, multicoloured umbrella. He brought it with him on a relaxing lakeside fishing trip. (TV: The Two Doctors) He also used it at least once as protection, while about to be stoned. (TV: The Trial of a Time Lord: The Mysterious Planet) He last had it with him when he crash-landed on Lakertya and regenerated. (TV: Time and the Rani)

Seventh Doctor
The Seventh Doctor initially carried his previous incarnation's multicoloured umbrella, at one point clumsily brandishing it as a weapon against the Rani. He left it behind upon choosing his new outfit. (TV: Time and the Rani)

After his regeneration stabilised the Doctor generally continued to carried an umbrella as part of his day-to-day outfit, whether the occasion called for it or not. He initially carried a black umbrella with a handle. (TV: Time and the Rani, Paradise Towers) Eventually he acquired a new umbrella, with an elaborate handle in the shape of a large red question mark. (TV: Delta and the Bannermen)

On the planet Svartos, the Doctor saved himself from slipping off a sheer ice cliff by hanging from his umbrella. (TV: Dragonfire)

The Doctor was known to measure objects with his umbrella. (TV: Remembrance of the Daleks)

The question-mark umbrella handle was known to split in half and unfold into a seat, allowing the Doctor to plant the umbrella into the ground and use it as a makeshift stool. (COMIC: Planet of the Dead, PROSE: Storm Harvest )

A secret compartment in the Doctor's umbrella concealed a vial of Gallifreyan restorative. (COMIC: The Forgotten)

When not in use, the Seventh Doctor's umbrella could often be seen resting on the hatstand in the TARDIS console room.

The Eighth Doctor gave Bernice Summerfield this umbrella, when they met each other after he regenerated. (PROSE: The Dying Days)

Eighth Doctor
According to Alan Turing, the Eighth Doctor carried a yellow and white umbrella with what Turing called a "very fine" maple-wood handle shaped like a duck's head. (PROSE: The Turing Test)

The Doctor found in the TARDIS a yellow umbrella with a question mark handle which contained a concealed sword blade. He claimed it had never been drawn, but was unsure if it was actually his. (PROSE: The Slow Empire)

Tenth Doctor
While the Tenth Doctor did not typically carry an umbrella, he appeared to make extensive use of the Sixth Doctor's multi-coloured version while on rainy Grått. (COMIC: The Whispering Gallery)

Eleventh Doctor
The Doctor compared the patchwork people Auntie and Uncle to his old umbrella. (TV: The Doctor's Wife)

He used a simple black umbrella as a bit of a test for Clara Oswin Oswald. She quickly deduced that he needn't have been carrying an umbrella at all; the only reason he had thrown it at her was so she'd have something with which to pull down the TARDIS staircase. (TV: The Snowmen)

Companions Umbrellas
Clara Oswald used an umbrella while it was raining at Caliburn House

Behind the scenes
The so-called Shalka Doctor kept a plain black umbrella in an umbrella stand, which the Master had a habit of leaving in the TARDIS' zeppelin hangar.