Big-Lipped Alligator Moment: Some fans felt that the "Dan and Chris" skit from "Camping" are like this. They doesn't seems to contribute to the plot by much on that skit and it never brought up again.
Crosses the Line Twice: Mr. Higglesworth is the embodiment of this trope. Many jokes and snarks he quips that otherwise would be offensive for it's worth are so overdone that it became really funny.
Emo kid overdose himself to submission in "Pep Rallies".
The attendance scene from "Field Trips".
Ensemble Darkhorse: Elmer J. Fapp is a big example. He only has few lines that you can count with your fingers on his debut. Many liked his antics so much that eventually he became the mainstay of the main cast line.
Mr. Higglesworth is rude, sadistic, and a drugged man who has no problem of crossing the line like he care. Otherwise he is an exaggerated fit of stereotypical Sadist Teacher archertype that shouldn't even qualified as a teacher to begin with, yet for some reason many liked his skits and making him one of the most popular teacher character in the show.
It's not hard to see why many liked Elliot's Grandmama on her only appearance in "Camping".
Growing the Beard: As the series went on, Kitty's skills in Machinima creation grows exponentially, with each episode felt distinct and more polished. Special mention goes to "Pep Rallies", where the editing is a lot tighter, the voice acting is more expressive, the comedy is more well placed, and introducing two more characters for the main cast line. And it's achieved within short time of 67 days!
The Woobie: Some of the teachers, most notably Mr. Cool and Mrs. Person can be seen as this.