At the beginning of the twentieth century, no man of quality would have been seen without a walking stick any more than he would have been without a hat. The practice continued among well-dressed men until it virtually disappeared in the 1970s. Today, as you know, hats are rare and the walking stick virtually extinct on the street.
Classic cane styles include crooked Malacca for city day wear, ivory trimmed ebony for evening and knobbed blackthorn for the country. Those are the three that I have currently, and I hope to find examples of bamboo and one or two others eventually. Great versions of anything are difficult to find but canes are readily available at antique dealers and on eBay, and should be collected in advance of need. When one can no longer walk unaided it is rather late to begin shopping.
Of course, it is a brave man that carries a stick when healthy, though they can serve to give the disapproving a good thrashing. For self-defense was the secondary function of the cane after swords were banned in most jurisdictions (wielders should review the Beginners Guide to Using the Cane and related publications). But all it takes is a convincing limp to warrant carrying one.
A stick is just dandy. If you've twisted your ankle.