Ken Levine recalls a M*A*S*H episode which had the same plot as an earlier episode. The staff realized this only after the episode had already started filming. I join with many of Ken's readers in thinking that the unintentional remake was actually a better episode.
TV shows unintentionally recycle their own plots all the time. Of course they also intentionally recycle plots. And sometimes it's hard to tell which is which. I knew about the similarity between those two M*A*S*H episodes, but until I saw Ken's post I had no idea if this was intentional, unintentional, or somewhere in between, because these things fall into three categories:
a) The show does an episode with an unintentional similarity to another episode. See above. See also Pinky and the Brain, which did a half-hour episode around a story that had already been done as an Animaniacs short, but the people involved with the episode claimed they hadn't seen the original short.
b) The show intentionally recycles another episode, figuring that most people won't remember it (obviously this was much more common before everything started getting syndicated). Bewitched was the king of this tactic; as early as their third season, they were re-making episodes from the first season.
c) The show independently comes up with something similar to an earlier episode, someone on the staff recognizes this, but it's decided that the new story is sufficiently different from the old one (The Simpsons is always doing episodes that are sort of, but not quite, like the old ones).
Then there are all the shows that recycle episodes done by other shows. Again, it's hard to tell, without knowing for sure, which of the three above categories these things fall into, especially when the two shows are from the same production company. For example, I remember that Just Shoot Me, an NBC show produced by Brillstein-Grey, did an episode where Elliott (Enrico Colantoni) coaches Nina (Wendie Malick) for a radio interview by teaching her some big words she can use to make herself sound intelligent; the words are all ridiculous fake words, and when she uses them on the air, she sounds like an idiot. This was the exact plot that had already been an episode of NewsRadio, which was an NBC show produced by Brillstein-Grey. But did the writers of Just Shoot Me actually knock off NewsRadio, or was it just an idea that was floating around (it is something that two people could come up with independently, after all)? We'll never know.
And yeah, I bring that up in part as an excuse to direct your attention to the funniest NewsRadio ever.