Umbrella
The Doctor's umbrella was one of several umbrellas owned by the Doctor.
The Sixth Doctor was known to occasionally carry a bright, multicoloured umbrella. He brought it with him on a relaxing lakeside fishing trip. (DW: The Two Doctors)
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 question mark. (DW: Delta and the Bannermen)
When not in use, the Doctor's umbrella could often be seen resting on the hatstand in the TARDIS control room.