A staple of the American family-oriented Sitcom, the Golden Moment usually occurs in the last few minutes of the episode, when An Aesop is delivered. After 20+ minutes of hijinks and confusion, Dad sits down with Junior for the following exchange:
Junior: I guess I screwed up, didn't I?
Dad: I guess so.
Junior: None of this would have happened if I hadn't been trying to impress people. I just wanted so much for them to like me.
Dad: Son, anybody who doesn't like you for who you are isn't worth trying to impress.
Junior: Gee, you're right dad. From now on I'll just be myself.
Also Lampshaded in one episode where JD is putting his Inner Monologue down in his diary and leaves. A few seconds later, the Janitor breaks into his locker to read the diary and mocks it.
Surprisingly, The Odd Couple was often guilty of this. Many episodes, especially early ones, would end with Oscar and Felix each admitting that the problem was the result of their respective sloppiness and pickiness, and reaffirming the importance of their friendship.
Subverted and played for laughs in an episode of Eureka, wherein Carter and his daughter have a moment, complete with sappy music...at which point they demand to know where the music is coming from, and then leave when the AI controlling the house owns up.
Series.The Facts Of Life owned this trope, playing it so straight they frequently didn't even bother with the lighten-up gag. Or if they did, it came through brave tears.
Lampshaded in Arrested Development: Michael and George Michael, his son, are making snacks and discussing their plot of that episode. George Michael remarks that he doesn't need his dad to stay out of his life, he's the biggest part of his life. Michael states, refering to the snack they are making, "That's a little cornball, son."
Happy Days has an episode in season one where, after going through gang initiation which involved pulling pranks on a policeman, stealing their principal's toupe, and going to a sockhop in dresses, Potsie and Richie realize that Mr. Cunningham was right—they didn't even like the guys they were trying to impress and should have just been themselves all along. Mr. C then comes in and has a little chat with Richie which ends on a corny joke.
Averted in the very first episode of The Cosby Show, when Cliff is trying to get to the bottom of Theo's terrible grades and Theo makes a heartfelt plea for understanding, pointing out that while Cliff and Claire are, respectively, a doctor and a lawyer, Theo doesn't love them more or less because of that, and maybe his parents should accept the fact that Theo is just 'a regular person' and love him anyway. As the studio audience begins to 'awww...' Cliff reacts silently for a second, then yells, "That's the dumbest thing I ever heard!" and proceeds to tear Theo a new one for not even trying.
Parodied in nearly every episode of Moral Orel, in which Orel learns a twisted Aesop after a beating from his alcoholic father.
Seth MacFarlane in DVD commenteries has termed this the 'moment of shit', and as such has subverted it quite a few times in Family Guy, usually having the father Peter fail to get the lesson at all and say something inappropriate.
It's also subverted a lot in American Dad!. To cite one example, in the episode "Haylias", Stan tries to brainwash Hayley so she'll start behaving like he feels a woman should, but a bug in the program causes her to want to kill Stan instead. As Hayley holds him at gunpoint, Stan sees the light and apologizes to Hayley for trying to control her life. She shoots him in the head.
South Park plays with this a lot. Sometimes it seems to be played almost straight. Other times they make satire out of how seriously the townspeople seem to take it, when it's not a real/decent moral at all.
Almost THE EXACT exchange of the example, or at least the exact scenario, occurs at the end of A Goofy Movie.
In the first season of Garfield and Friends, several of the Orson's Farm segments had one of these, usually in song and dance form. The show got rid of them later.
Parodied on Aqua Teen Hunger Force when Meatwad watches the other characters in a "sitcom with a sci-fi/horror twist" on an apparently cursed television. It comes complete with sitcom-style "Awwwww" from the audience, followed by a lame joke with laugh track. Meatwad appears to be the ideal television watcher, though, declaring "I identify with that!"
Played completely straight (except for maybe one episode) at the end of most My Little Pony: Friendship Is Magic episodes. Earlier seasons had it in the form of a "friendship report" written by Twilight Sparkle (and later her friends as well) to Princess Celestia, while Season Four has the cast keeping a diary of what they've learned.
In Thalia's Musings, Apollo attempts to invoke this trope after Thalia has a narrow brush with Hera's wrath. Thalia can't take it seriously and doubts he does, either.
Apollo: Well, that's the end of that. I hope you've learned something.