This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Family Matters
Carl visits the grave of an innocent man who was killed during a hostage situation one year prior. He feels it was his fault since felt he didn't do anything to save the man and as the episode progressed, he was taking all of his frustrations and anger out on the family and people around him. While he's at the gravesite and apologizing his heart out, the late man's wife arrives and forgives him as they comfort each other.
Harriette: It wasn't your fault.
Carl: I know that up here...(points to head)...but not down here (points to heart).
The man's widow explaining to Carl that she understands how he feels; on the night of her husband's death, she had playfully pestered him about having a craving for ice cream, and after feigning a complaint he decided to go anyway...then the hostage situation happened. She had spent much of that year afterward blaming herself, believing that if she hadn't asked him to go to the store that night he wouldn't have died.
Widow: And so he walked out the door and...left my life...
Harriette and Rachel reunite with their father, who they hadn't seen since they were kids. Rachel is alright seeing her dad because she was so young before he left, but Harriet got to bond with him a lot more. She's heartbroken and hurt that her daddy would lie and abandon her as a child.
Harriette: Why weren't you there when we needed you?!
Laura finding out that her campaign for a Black History class is only fanning the flames of hatred.
A note in Laura's locker: "If you want black history, go back to Africa."
Plus Carl and Harriette's discussion of racism and this whole predicament.
Carl: People that did this to us are teaching that same garbage to their kids.
In order to help Laura through this, Estelle tells her a touching story of when she was growing up. She loved to read, but could not use the town library because it was for whites only. Estelle explains that the first time she tried to go in, the librarian- someone she knew personally- pushed her into the street and told her to never come back. She went back every day for six months- enduring staring, name-calling, and spitting- until one rainy day, the librarian shook his head and handed her a library card.
Estelle: And, from that day forward, everyone could use that library.
Waldo's defeated, repeated, "Aw, gee," when Maxine mistakes Eddie's messing around to mean that Waldo is too, and you see how broken up he is when he thinks the girl he loves hates him.
Good thing they get back together thanks to the two girls who Eddie invited over helping to clear things up. You even find yourself cheering when the girls become disgusted by Eddie's unsympathetic attitude.
A Real Life one. Michelle Thomas, who played Myra, was struck with a rare stomach cancer during the eighth season, which was why she appeared so sporadically during the final season. She put off some of the more extreme treatments because she wanted to have a family and the treatments would have rendered her sterile. She died only a few months after the series ended.
There is another meta Tear Jerker: This show was an instance of the cast finding out the hard way that the sets were destroyed and the series was cancelled.
One episode has Steve and Carl sharing a hospital room—Steve has appendicitis, Carl got shot in the butt. (Yes, really). After characteristically annoying Carl beyond all reason for the whole episode, Steve saves his life. It turns out the "doctor" overseeing Carl's case was the angry sibling of the criminal who shot Carl in the butt, whom he arrested. Later that day, the family comes to visit. Laura stays behind, hugs Steve, and tearfully says, "Thanks for saving my daddy."
Any interaction wherein one of the Winslows tell Steve off or otherwise finally exhaust his ability to take their shunning. The sleepwalking episode gets special mention because Steve needed a hypnotist to get to the bottom of things.
This also applies to any time someone calls Waldo an idiot or otherwise seriously dents his self-esteem.
In "Good Cop, Bad Cop", Carl has a confrontation with a racist officer who pulled Eddie over because he was a black teenager in a white neighborhood. After the cop leaves, Carl has a chat with the man's rookie partner:
Carl: You like being a cop? Officer Carmichael: Yes, sir. Carl: Why? It's a very dangerous job, you put your life on the line every day, and you never get credit for it. Officer Carmichael: Yeah, well, I just thought I'd make a difference, you know? Good guys against bad guys. Carl: Well, that's a very good reason. Just one problem, son: your partner is one of the bad guys.
Laura Urkel, full stop in "It's Beginning To Look a lot Like Urkel". Although some fans considered it Narm and Laser-Guided Karma for Laura, you can't help but sympathize with her for happening at Christmas and being rejected once and for all so cruelly by Steve, who has switched places with her due to an angel giving her a taste of what it's like to be him.
Laura: I'll go, but I'll never stop loving you. *walks out the door* Goodbye, forever.
Steve: Goodbye, and good riddance!
*door slams and a bunch of snow falls on her head, as she stands outside looking like she's about to cry*
The episode where Laura's date, Ted, tells everyone that they had sex. Made even worse it you ever had your reputation ruined because of a lie, especially if it came from someone you thought you could trust, like Laura did. Harriet even found her crying on the back porch about it. It's also has traces of being Crowning Moment of Awesome and Heartwarming Moments due to Steve telling her about it after he overheard Ted brag to his buddies and trying to stop it (and her not believing him) and Eddie threatening to beat him up if he didn't retract the rumor.
Carl accidentally being electrocuted while trying to fix a lamp, which also doubles as Nightmare Fuel. Luckily, Steve was there and knew CPR, which saved him. In addition, it was one of the few episodes where everything was completely serious, with little to no laughs.
"The Gun" features a realistic look at bullying and guns, as Laura is beat up by a female bully and her friends for her jacket and another girl ends up being shot because she refused to give the bully her shoes. Even worse, Maxine is comforting the traumatized girl and crying as she holds her and tries to stop the blood loss from her arm, "Why didn't you just give her the shoes?!" while Steve calls out for someone to call an ambulance. And the worst of it all? Laura was seconds away from purchasing a gun (for self-defense) from a sleazy student before the girl was attacked.
Carl and Harriet's talk afterward, with both of them realizing that their kids' generation now has a lot worse to worry about than they did at that age.
While almost always played for laughs, any talk of Steve's home life is quite sad. For all the complaints from the Winslows, they at least like him when he's not causing trouble and can get along with him; his unseen parents not so much. They charge him rent, constantly avoid him, don't feed him every day, and only seem to tolerate him because they're legally required to. In the hyponotism episode mentioned above, Steve recalls his birth and that his father tried to push him back into the womb. While they didn't move to Russia just to get away from him, they clearly didn't mind that he chose to stay behind. No wonder the guy is so screwed up.