First Doctor's cane

The First Doctor possessed at least two canes, (PROSE: Echoes of Future Past, The Arboreals, A Big Hand for the Doctor) also called walking sticks, (PROSE: The Exiles, Bide-a-Wee, AUDIO: Quinnis) which he sometimes brought with him when he ventured out of his TARDIS. (PROSE: The Arboreals, Quinnis)

One featured a twisting design at the top of the shaft (TV: Marco Polo, etc.) and the other did not feature this design. (TV: The Massacre, The Five Doctors, etc.)

Uses
Apart from the obvious use in assisting with walking, the Doctor's cane was sometimes used as a means of defence. (PROSE: A Big Hand for the Doctor, AUDIO: Quinnis, The Secrets of Det-Sen)

Description
The cane had a twisted shaft and an L-shaped silver handle. (TV: The Keys of Marinus, PROSE: The Sorcerer's Apprentice)

History
Shortly after escaping Gallifrey with his granddaughter Susan, the First Doctor slept with his hands on the handle of his cane. (PROSE: The Exiles)

Later, he used his cane when he ventured out onto a planet with Susan. (PROSE: The Arboreals)

When confronting the Soul Pirate Igby, the Doctor kept his cane stretched out in front of him as a means of defence, however Igby easily battered it away with his silver wrist-guard. (PROSE: A Big Hand for the Doctor)

The Doctor had his cane with him when he ventured out onto Quinnis, at one point raising it up in front of him to fend off a Shrazer. (AUDIO: Quinnis)

While living at 76 Totter's Lane, the Doctor used his cane to prod at some rubbish on the ground. (PROSE: Echoes of Future Past)

The Doctor used a cane in 1289 Cathay, after his journey by horseback from Cheng-Ting to Shang-Tu had left his body sore and aching. (TV: Marco Polo) Shortly after departing Peking, the Doctor travelled to and used his walking stick once again. (PROSE: The Sorcerer's Apprentice) On a visit to ancient Egypt, it saved the life of pharaoh Menkaure when the Doctor accidently blocked a poison dart with the stick while explaining it's purpose.

Many lifetimes later, the Tenth Doctor found his walking stick cane enshrined as the primary possession of his first incarnation in a "museum" within the TARDIS Matrix. When suffering from memory loss, touching the cane restored his recollections of the First Doctor's life, and he recalled the cane's role in saving Menkaure in particular. It would later be used alongside his other incarnations' possessions to give form to the First Doctor in the Time Lord's final confrontation with Es'Cartrss. (COMIC: The Forgotten)

Behind the scenes
Through the production of his era of Doctor Who, William Hartnell used at least two separate walking sticks.

The more iconic can be seen in such stories as TV: The Massacre and The Reign of Terror. However, another can be seen in one photo taken of Hartnell on the set of TV: The Massacre. This cane is nearly identical to the one used by Richard Hurndall in TV: The Five Doctors.