(covers information from several alternate timelines)
This page contains information regarding Star Trek: Picard, and thus may contain spoilers.
A cane or walking stick was a stiff rod with a curved or handled top used as a support for walking, or for ensuring that an intended path for a blind person remained obstruction-free.
A year after Nero released Centaurian slugs into his mouth and after having them removed from his brain stem, Admiral Christopher Pike still required a cane to walk around with. (Star Trek Into Darkness)
In revealing a hard truth to Zefram Cochrane, Doctor Leonard McCoy described the Companion's interest as that of love. In fact, McCoy thought it was so apparent that "a blind man could see it with a cane." (TOS: "Metamorphosis")
Upon returning to Deep Space 9 after losing a leg in the siege of AR-558, Nog walked with the support of a plain, metallic cane. Because he continued to use the cane despite his medical status, Nog was particularly sensitive to its use. When talking to Ezri Dax, Nog referred to "the 'cane problem,'" and further said, "You're about to ask me why I need to walk with the cane, since Doctor Benbasset told you my biosynthetic leg is working perfectly. He also told you the problem's all in my head, that I'm crazy." In an effort to wean Nog off his dependence on the cane, Vic Fontaine gave him a replica of a cane used by Errol Flynn. Nog commented that the cane, complete with a button-controlled flicker of flame, was reminiscent of the Grand Nagus' staff. (DS9: "It's Only a Paper Moon")
In a vision from the Prophets that Benjamin Sisko experienced in 2374, his persona of Benny Russell used a cane, after he tried to fight his way to Jimmy, who had just been killed by police officers Burt Ryan and Kevin Mulkahey. (DS9: "Far Beyond the Stars")