Umbrella

The Doctor's umbrella was one of several umbrellas owned by the Doctor.

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)

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.