This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Wakko's Wish
Seeing the usually-zany Warner Brothers having to be mature and responsible for their sick sister is sobering enough, even if it is played for laughs at times. But the ultimate Tear Jerker of the movie is most definitely the final run for the star where Dot is hit by a cannonball, and the heartrending "No!" from her brothers as they see her crumpled, unconscious form half-buried in the snow. The entire town listens in complete silence as she has Yakko tell her the story "one last time." Yes, she gets better, but the image of Yakko cradling his dying sister and trying to keep his composure while telling the story, then breaking down in tears as she finally "dies" is burned into many a kid's brain.
Well, yeah. Apart from the apparent "death" itself, seeing Yakko cry will do that to people.
Hell, even some of SALAZAR'S MEN were crying over her "death!" The Captain of the Guard even calls Salazar out on it!
Captain: She was the cute one, man! The impossibly cute one! You killed her, man! Wrong, wrong!
Dot: I like that story.
Yakko: Goodnight, sis.
The nighttime scene in the Warners' broken shanty.
Wakko: If I only earned more.
The notion that the King and Queen are the Warners' parents.
Watching everyone's reaction when Salazar first ordered the execution of the Warners'. Heck the kids handled it better than everybody else.
That and while not as bad, poor Plotz, Ralph and the Goodfeathers being arrested also counts.
Wakko's song about finding the wishing star have a very sad, desperate feeling to them that's very sobering when compared to the normally zany antics of the movie.
Wakko: Out in space, so bright and clear / Can you see me way down here?
Meta-example: This was the last project Richard Stone worked on before his death from pancreatic cancer in 2001. Gone too soon, indeed.