Umbrella
The Doctor's umbrella was one of several umbrellas owned by the Doctor.
Fourth Doctor
The Fourth Doctor occasionally kept an umbrella in his console room's hatstand. (DW: Destint of the Daleks)
Sixth Doctor
The Sixth Doctor was known to occasionally carry a brightly multicoloured umbrella. He brought it with him on a relaxing lakeside fishing trip. (DW: The Two Doctors) He also used it at least once as protection, while about to be stoned. (DW: The Trial of a Time Lord:The Mysterious Planet) He lastly had it with him when he crashed-landed and regenerated. (DW: Time and the Rani) It was later left behind on Lakertya by the Seventh Doctor during wardrobe change.
Seventh Doctor
The Seventh Doctor usually 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 whangee handle. (DW: 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. (DW: Delta and the Bannermen)
On the planet Svartos, the Doctor prevented himself from slipping off a sheer ice cliff by hanging from his umbrella. (DW: Dragonfire)
The Doctor was known to measure objects with his umbrella. (DW: 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. (DWM: Planet of the Dead, PDA: Storm Harvest )
When not in use, the Seventh Doctor's umbrella could often be seen resting on the hatstand in the TARDIS console room.
Eleventh Doctor
The Doctor compared the patchwork people Auntie and Uncle to his old umbrella. (DW: The Doctor's Wife)
Behind the scenes
The non-canon Ninth Doctor kept a plain black umbrella in an umbrella stand, which the Master had a habit of leaving in the TARDIS' zeppelin hanger. (WC: Scream of the Shalka)
