Any time Cliff and Clair share a romantic moment. Doubly true if it takes place after they'd been fighting or had an argument during the episode.
In the pilot, Cliff still manages to give a heartwarming speech to Theo immediately after telling him that what Theo had just said was the DUMBEST thing he'd ever heard.
Cliff's initial response to Theo's speech subverted the CMOH that everyone was expecting Theo's speech to be.
But after he's done chewing him out, he hugs him and says he loves him. Of course, he plays with the audience again by adding, "And maybe your mother loves you, too."
Clair convincing Rudy that being 5 years old doesn't mean "Being nothing."
Theo giving Cliff's acceptance speech for the Physician of the Year award.
The uncut version of the episode has Dr. Wexler (Sheldon Leonard)'s speech about why Cliff won the award as well.
Cliff and Denise having a dance together after an episode where they spent pretty much the entire time arguing with each other.
Both this and a Crowning Moment of Awesome for Theo comes in the episode "Theo And the Joint." Clair finds a joint in Theo's bookbag and asks him if it's his. He denies it, and that's enough for her. But it's not enough for Theo, as he hunts down the intimidating kid who put the joint in his bag, brings him back home, and has him tell his parents the truth. In response, Cliff looks at the other boy, says, "that's a big dude," smiles proudly, and gently punches Theo on the shoulder. There's a kid who understands the value of integrity, and a parent who respects it.
In the final episode, Denise writes a song that everyone else finds horribly depressing. She rewrites it at the end of the episode to be a tribute to her parents' love for her after receiving advice from Lena Horne. The lyrics themselves are a positive Tear Jerker.
Clair reminds Rudy that, no matter what may happen, she'll always love her.
Watching Rudy cuddle up to Clair the night after her Football team loses its championship game.
After getting all of Clair's questions wrong about the night he proposed to her, Cliff reveals that he really does remember the important things by instantly naming the title, artist, year, and number copies of the song that was playing on the radio.
When Clair breaks her toe, she takes out all of her frustrations over it on Cliff for the whole episode. The scene at the end where they make up and "table dance" together fulfills the trope.
Mrs. Westlake's farewell to Cockroach after he explains his (off-screen) Crowning Moment of Awesome during her class at school to her.
"It wasn't your class. It—it just wasn't your class."
The usage of Martin Luther King's "I Have A Dream" speech in "Vanessa's Bad Grade"; the episode debuted four days before the first time MLK, Jr. Day was observed as a federal holiday.
In "Denise's Friend," Denise asks Cliff to examine Michelle, who hasn't been feeling well lately. It turns out to be a bladder infection, but her unwillingness to go to her parents before finding out makes Cliff wonder if his own kids are also prone to keeping potentially big secrets. He and Clair sit down with Sondra, Denise, Theo and Vanessa to talk about this and about how they be fully honest with any problem/issue. After some funny moments, Cliff insists that while getting angry is always a possibility, he and Clair will love them no matter what and always help them with their problems.
Cliffs recounting the story of how his parents met and the unveiling of the commissioned portrait of them at their 49th anniversary party.
Clair's farewell speech to Denise right before she leaves for college.
Cliff and Russell's interactions during the final moments of "Cliff in Charge," especially when Russell tells Cliff his favorite bedtime story from when he was a kid again.
In Calling Dr. Huxtable Vanessa is really scared about Cliff getting angry that one of her friends was smoking in her room while Cliff was out. Cliff ends up relating to her about how peer-pressure while growing up can be really hard to deal with and ends up even praising her for the actions she did take when dealing with said friend.
Elvin's proposing to Sondra.
Mrs. Granger, one of Cliff's co-workers and friends at the hospital, who's about to be laid off due to cutbacks, telling him that her daughter has offered to put her through college as a "thank-you" to her mom for working hard to put "her" through college. In addition, earlier in the scene, Mrs. Granger telling Cliff about her grandson and how he wants to be a grandmother himself because "grandmas always give you presents." Later sets up a Tear Jerker moment when Cliff asks her what he he has to say about grandfathers, and Mrs. Granger sadly replies that he never met his as her husband married her simply because she was pregnant, and that he walked out on her on the first night of their anniversary. Later, though, she tells Cliff that on a brighter note, her daughter's husband is well more responsible and is taking his familial duties well to heart. All of this is made double by the fact that the actress playing Mrs. Granger, Rita Moreno, had previously co-starred alongside Cosby in The Electric Company.
After Theo overcomes his anger for not getting onto Dance Mania and taking his frustration out on the family, he's able to make up with them with no words needed.
Theo spends the first half of The Visit with cold feet and being unable to visit his friend Jake, a cancer patient, at the hospital. After several moments of awkward conversation, they're able to cut loose and have some fun until Jake gets worn out, lamenting how quickly he gets tired. By the end, he's newly resolved and determined to beat the disease.
The entirely improvised and ad-libbed scene between Sondra and Cliff after Sondra gives birth to her twins.
Cliff carrying Rudy to bed after she falls asleep from having stayed up late too many nights in a row.
Cliff telling his grandchildren about his dead brother, James Theodore Huxtable.
Ray Palamino (played by Sammy Davis Jr.) thanking Cliff from the bottom of his heart for giving him the opportunity to meet his great-grandchild especially after remembering that he'd mentioned earlier that he hadn't seen anyone from his family in nearly 20 years and after telling everyone around him that he's illiterate. This is immediately followed up with a retired English teacher (played by Arnold Stang) offering to teach Palamino how to read and write.
Davis died not too long after this episode aired. Throughout the seventh season, Cliff would be seen wearing a black pin with Davis' initials as a tribute to him.
Convinced that Denise is in no way ready to be a mother, Cliff and Clair head up to her room to check up on her, but back down when they find Denise cradling Olivia and reading her a bedtime story.
Martin takes the responsibility for not getting a reservation for quarters on his base when Denise was actually the one who didn't make the necessary phone call.
During the Thanksgiving dinner, Russel in no way hesitates to recognize Martin's ex-wife and Olivia's mother, Paula, as part of the family.
Denise inviting Paula to Thanksgiving dinner in the first place, with no hesitation on her part and despite everyone else's assumptions that she would (or should) be uncomfortable with it.
Denise is afraid that Martin's mother, Lorraine, can't stand her and spends most of the episode avoiding her. However, after the misunderstanding is cleared up, Lorraine assures Denise that they will become wonderful friends. Denise gives her a hug while calling her Mom in return.
Two moments during Olivia's birthday party: Martin telling Olivia how special her gift is because she's inheriting a tricycle that carries all of the good memories of its previous owners with it. After that, there's Martin taking the time to pull Denise aside and tell her how thankful he and Olivia are to have her in their lives.
The entire King of Romance contest, especially after the wives were planning to intentionally make fun of the husbands, but their hearts are softened by the thoughtful gifts given to them.
"It's All in the Game": Vanessa tries to cover up getting a minor car accident. Instead of having a big blow-up, the family discussion (which eventually involves the kids) turns into how much the parents do for them, and the kids countering with how they embarrass them, in a good-natured, hilarious, heartwarming 10-minute segment that reminded more than a few tropers about their own families.
Even though Cliff ends the segment by saying, "Well, at least I can drive," his laughter and physical expression show he's admitted defeat to everything else the kids had brought up.
"Cliff and Jake": Cliff learns about a longtime feud between his friend Jake and Jake's childhood friend Ernest wherein they haven't spoken to each other in years. However, Jake's daughter and Ernest's son are getting married and ask Cliff to mediate between their fathers to end the feud. It ends with the two men finally overcoming the problem and celebrating the good news about their children.
The very last shot of the final episode has Cliff and Clair dancing prior to him escorting her off stage, past the camera, crew and audience and out of the studio.
The brief series recap immediately after reminds everyone why they fell in love with the show in the first place.