This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Young Ones
The end. Yes, it's supposed to be funny, and they were all little rotten bastards... but it's just so sad, especially after they finally got the freedom they wanted (that's probably the point). And that sad "doo-wop" music that plays over the credits makes it so... poignant.
The credits. Many filmmakers have said that filmmaking is a group effort, that it's never one man's film, but it doesn't change the fact that the people who say this are usually the guys who are listed first in the end credits. But during the finale, the credits start, and there's no mention of who did what—everyone's listed alphabetically, regardless of their part on the program. For that one moment, while the program's in its death throes, everyone's equal. Even on a show about complete bastards blowing each other up and screwing each other over, there's something rather touching and poignant about that.
Same episode, the scene prior: Vyvyan accidentally running the Vyvmobile into a lamppost and realizing he had also unwittingly killed SPG, who was asleep on the radiator. His car and his hamster were the only two things he ever showed anything resembling affection toward, and he is absolutely crushed to lose them both — the only indication he ever gives on the series that he has a heart. Granted, he’s forgotten all about it a few minutes later, but still.
Neil repeatedly carrying down his pathetic birthday cake and shouting "Surprise!", only to be ignored every time. When he finally explains that today is his birthday, Mike replies: "Now you knew that anyway and we don't care, so where's the surprise?" Neil, understandably, looks totally crushed.
Rick's 'but I'm the People's Poet' speech is now poignant viewing, as Rik Mayall died at only 56.