The show ran from 1958-1963 and tries to embrace both the feel good values of the 1960s and the traditional values of the Western. This Wikipedia entry nails it.
The various episodes of The Rifleman promote fair play toward one's opponents, neighborliness, equal rights, and the need to use violence in a highly controlled manner ("A man doesn't run from a fight, Mark," McCain tells his son, "But that doesn't mean you go looking to run TO one!"). In other words, the program's villains tend to be those who cheat, who refuse to help people down on their luck, who hold bigoted attitudes, and who see violence as a first resort rather than the final option. Indeed, a curious aspect of the program is that when they meet African-Americans, the people of North Fork are truly color-blind. In "The Most Amazing Man", a black man (played by Sammy Davis, Jr.) checks into the only hotel in town; for the entire show, no one notices his race. Not only is this noteworthy for the 1880s setting, it was radical for Hollywood of the early 1960s. While the message was clear, it was neither heavy-handed nor universal. A certain amount of xenophobia drifts around North Fork, however, forcing McCain to defend the right of a Chinese immigrant to open a laundry ("The Queue") and the right of an Argentine family to buy a ranch ("The Gaucho"). This racial liberalism does not extend to villains, however. The Mexicans in "The Vaqueros" are indolent, dangerous, and speak in the way of most Mexican outlaws in Westerns of the time.
Thanks to the glorious interweb I know also know that the show's star, Chuck Conners played both professional baseball and basketball, having been on both the Boston Celtics and the Brooklyn Dodgers.
Anyway, I'm enjoying the reruns--much to the chagrin of my son who can't get over the corny dialogue. I don't know why it's appealing, exactly, but I do like the fact that it's a drama that's only a half hour long and it's shown without commercials but with the commercial fade outs so it's like a very short play in several acts. Maybe I just like seeing the hunky Chuck Connors shoot his rifle.