"Dead Man's Shoes" is the 18th episode of the third season of The Twilight Zone, and was first broadcast in January of 1962. It starred Warren Stevens as homeless man Nate Bledsoe. Although the episode shares its title with two British movies, this is coincidental.
The episode opens with two mobsters ditching a corpse in a section of New York's Bowery, where a homeless man soon notices the titular shoes, and takes them from the corpse to replace his own ragged shoes. Soon enough, he notices personality changes, changes that seem to lead him to taking on at least part of the dead man's memories and personality. And given that the man was recently murdered in a gang killing, this probably will not end nicely.
One of the things that struck me about the episode is that, much like "The Jungle", it seemed like a missed opportunity. The Twilight Zone is, as its name implies, often a story about what happens in-between. This episode's premise is that by adapting an external appearance, in the form of a pair of shoes, someone can change totally. As a concept, this is more interesting than what this episode does turn into: a standard mob revenge story. However, with that, it is still well done, and I especially noticed the continued improvement of The Twilight Zone's "noir" stories over such first season episodes as "The Four of us Are Dying".