You ever notice how many episodes of The Andy Griffith Show have been raided by other shows for story material? I've only had the season 3 DVDs for two days and already I've watched two episodes that inspired storylines on later shows. In the season opener, "Mr. McBeevee," Opie meets a man who is repairing a telephone line out in the woods; since nobody else has seen the man, everybody assumes that Opie is just making up his story about having a friend who lives in the treetops. This plot has been re-done a number of times, but most recently on "The Simpsons," where Homer made friends with a repairman whom nobody else had met, and everybody figured Homer just had an imaginary friend. The other episode that inspired something semi-recent -- though this was arguably as much a parody as a borrowing -- is the episode where a man causes a traffic accident but can't pay the damages, so he works off his debt by becoming Andy's valet. That's clearly the inspiration for the plot of Jerry's failed sitcom pilot on "Seinfeld": a man crashes into Jerry's car and can't pay the damages, so he becomes Jerry's butler.
"The Honeymooners," "I Love Lucy" and "The Dick Van Dyke Show" are other shows that get raided all the time, usually by lesser shows. To name one example: I remember seeing, as a kid, an episode of "Perfect Strangers" where a hypnotist tries to hypnotize Mark Linn-Baker, fails, but accidentally hypnotizes the guy in the other room, Bronson Pinchot; the post-hypnotic suggestion leaves him believing he's Elvis Presley whenever the phone rings, and going back to normal whenever it rings again. Only later did I discover that this was stolen beat-for-beat from an episode of "The Dick Van Dyke Show" (except in that one, Rob was hypnotized into acting like he was drunk).
In the drama field, action/adventure shows used to steal from each other all the time, particularly those produced by Universal, which shared a pool of writers who all needed to come up with lots of story ideas very fast. My favorite example of this: in 1982, Universal's "Knight Rider" did a show called "Good Day at White Rock" where the hero rides into a small town that is being terrorized by an evil biker gang, and helps the sheriff end the biker gang's reign of terror. The very next year, Universal's "The A-Team" did an episode called "Black Day at Bad Rock" where the heroes ride into a small town that is being terrorized by an evil biker gang, and help the sheriff end the biker gang's reign of terror. For all I know they might even have used the same set for the town.