This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Rocko's Modern Life
Tickled Pinky, which seems to be tailored to wringing tears from people who've lost organs, of all things. Rocko is put into surgery, where he has a dream about hanging out with his appendix. Rocko wakes up, and is horrified when he finds out that they removed his appendix. Fortunately, he gets to see Pinky go up into heaven, along with all his baby teeth and tonsils.
Followed by an anti-tear jerker moment when Heffer (who has had all the fat sucked from his body because the doctors thought he was there for an emergency liposuction) says good-bye to his fat, who tells him to "Get bent!"
The scene in Cruisin' where an old guy explains to Rocko about how old people are grumpy because they lost loved ones and Rocko starts getting tears in his eyes.
In "Kiss Me I'm Foreign", Filburt has to pretend he's married to Rocko to prevent him from being deported. A few scenes later, he has to break up with Dr. Hutchison. Seeing the normally perky Hutchison and Filburt cross paths with sadness in their eyes can get rather depressing. Thankfully, they get back together in the end when Rocko gets his green card.
The final scene in "Leap Frogs". After an entire gut-bustingly hilarious episode of Mrs. Bighead trying to seduce Rocko, she suddenly becomes a sympathetic figure when Mr. Bighead comes home and insults her openly. Rocko then, despite having a great disgust for Mrs. Bighead, kisses her on the hand and tells Mr. Bighead that Mrs. Bighead is a fine woman who can have any man she wants. Mr. Bighead gets jealous, but then realizes that Rocko is right and Bev and Ed make love by breaking plates with their tongues). The scene is a defining moment for Rocko, but one that many for years didn't get to see. It was a banned episode (only after three airings) but probably one of the finest of the series.
The scene in "Power Trip" where Really Really Big Man has Rocko take a look inside his nipples to gaze at his future self. Rocko quickly becomes ashamed of what he has become and tearfully hugs Filburt when the latter walks in all bandaged up as an apology for the way Rocko treated the turtle.
Several episodes of the show made Ed Bighead out to be a humongousJerk Ass, but some seasons delve into exactly why he might be cranky. He had a strained relationship with his son, is depressed because he feels too old and was no longer the toad he used to be. The episode where Bev accidentally gets a new nose strongly implies that his love for his wife is one of the few things he has left - when she couldn't go near him because of his horrid body odor, both were reduced to tears, and worse yet was when he thought his wife died, which cause him to have a severe meltdown. Remember that moment in "Cruisin'" where the senior gives Rocko a lecture as to why old people are so miserable? Ed's been there.
"Who's For Dinner," where Heffer is devastated to learn that he was adopted.
George: Now, Heffer, I'm still your father. Heffer: You're not my father! You're just some jerk in wolf's clothing!
In "Rocko's Modern Christmas," Ed makes sure no one goes to Rocko's party. Worse, no one cancels on Rocko, leaving him waiting with Spunky for hours for someone to show up. Then he tries to call his family, but all the lines are busy.
Rocko: And it didn't even snow. I don't think I'll ever find any Christmas cheer.