"The Execution" is the 26th episode of The Twilight Zone, first broadcast in April of 1960. It starred Albert Salmi and Russell Johnson (most famous as The Professor on Gilligan's Island).
The episode begins with a description of the life and imminent death of Joe Caswell (Albert Salmi), a thug in the Old West. Just as Caswell is about to die, the hand of fate intervenes, and he finds himself summoned by time travel to the middle of the 20th century, where a professor (Johnson, before he was "The Professor") is testing his time machine. Caswell is mystified by the new world he finds himself in, but quickly resorts to his thuggish ways. Through a series of coincidence, justice is served, although not at all in the manner that could be expected.
Most Twilight Zone episodes have a moral or lesson that is apparent and (given the nature of the show) relevant. I didn't really know what this episode taught me: that I should be more careful about what I pick up with my time machine? Perhaps it is just that even disturbed, time will still serve out the process of justice. But mostly I think it is that you shouldn't just pick someone out of the timestream without finding out who they are, first. Also, like many Twilight Zone episodes that try to be noir and streetwise, it fails to be very rugged and shocking for an audience in the present day.