Theo gives a whole seemingly heartwarming speech about how it doesn't matter if he doesn't succeed in school because Cliff should support him anyway because he's his son. Cliff responds: "Theo, that is the DUMBEST thing I've ever heard in my life. No wonder you get Ds in everything!"
What makes it even funnier? The audience had just finished applauding Theo's speech.
To put it in context, sit-coms in the 70's were absolutely rife with the "you should accept me no matter what I do" speech because of the whole generation gap thing going on at the time. And in every other sit-com, the scene ended with the older person giving in gracefully and a great big hug and hearfelt music and so forth. The audience reaction was absolutely typical for the time and everybody watching the episode was waiting for the hug. So when Cliff answers the way he does, it was unexpected and hilarious—listen closely and you'll realized that the laughter was very shocked laughter. This troper saw the episode with family when it first aired and we all just looked at each other like "what just happened?"
Bill Cosby mentioned that he was worried about whether the show would succeed or fail based on that one moment. But once the pattern was broken and the audience reacted positively, he knew that the show would be a success from that moment on.
How Cliff blackmails the older kids into attending the funeral for Rudy's dead goldfish.
The funeral itself counts too.
From the moment Theo reveals the shirt that Denise made for him up until the very end of that episode. Especially when Theo thinks he's avoided "The most embarrassing moment of his entire life" when instead he ends up walking right into it! Cliff trying to cover for him is a hilarious Crowning Moment of Heartwarming at the same time.
The story of Cliff trying to straighten his hair to impress Clair.
Plus the follow-up story of Russell's attempt to woo Anna by getting her [misspelled] name tattooed on his chest. He had to get it removed, leaving a large scar.
Cliff: "You told me that you got that scar during World War II from a German Nazi panzer attack."
Cliff talking to Theo about the olden days and how the father would run over his son with a plow if the son asked how much he'd get paid to do chores around the home.
Cliff's imitation of Clyde's singing.
Cliff's description of Theo's messy pizza-eating habits.
Cliff is sitting in court to watch Clair taking on a case. During the trial he and another man talk about how beautiful Clair is and Cliff pretends to not be her husband until he asks her out for a cup of coffee and then to get married. Clair accepts and the look on the other man's face is priceless.
Various pregnant women describing revenge dreams against their husbands. It's Turned Up to Eleven when Clair and one of her friends discuss theirs in Spanish and Cliff knows full well what they mean only by their pantomime actions.
"Breaking with Tradition" has lots of these moments:
Cliff explains to Theo that he doesn't want to be bothered and the boy takes it to heart... by later not letting Grandpa Russel Huxtable in the house when he shows up for a visit. Cliff's irritated reactions to Theo's genuinely being so clueless are priceless.
Moments after this, Cliff gets a phone call from Russel.
"Now, Dad, why are you at the neighbors'?"
Cliff telling Denise how much of a Determinator Russel was during the war. Russel held position in a trench near an enemy pillbox and would've easily picked off anyone outside, so the enemy just hunkered down to wait him out. Russel in response sought to out wait them.
Cliff: And my father sat there with one eye closed and one eye open, never blinked, and he waited and waited and waited and waited and waited. And the enemy figuring no human being on the face of this Earth could wait that long finally came out. Denise: And Grandpa shot 'em? Cliff: Nope. Because by that time, the war was over.
Doubles as a Brick Joke when Russel uses the same punchline for the story at the end of the episode.
Cliff admitting the only reason he went to Hillman was because Clair was going there, as he didn't trust the admittedly attractive male students. Cliff also states that he never told Clair this. ("Because I'm saving that for when I really get in trouble.") His attempt to keep Russel from purposely blowing the secret is also humorous.
The uncut version has Cliff and Russel talking about how Russel had the same talk about Sondra going to Hillman and Cliff doesn't want him to talk to Denise because last time involved "Lots and lots of crying!" To which Russel replies:
Russel: "Well I'm not gonna cry this time."
Everything involving Peter at the slumber party in his introductory episode.
How he got into the party in the first place: He was playing outside when Cliff told all of the kids to get in line and go inside, so he just went with the flow.
Cliff asking him how it feels to be the only man with seven women.
Four words: The Bucking Horse scene.
After Rudy spills a bag of flour, she runs out of the house and Clair follows, leaving Denise and Vanessa behind.
Vanessa: *Looking like she's ready to dive right in and start making snow angels.* "Really?"
Cliff is found guilty of "Contributing to the delinquency of a 6 year-old" and sentenced to "Appliance probation." Clair keeps a completely straight face during all of this until the very end.
Earlier in the same episode, there's this quote:
Clair: "Machines can be hard to resist sometimes: They're shiny, they make terrific noise, they've got those buttons that light up. That's why your father likes them."
There's also another gem from the episode, after Rudy causes a giant mess in the kitchen with the juicer. Theo and Denise walk in on the mess and decide not to clean it because Rudy wouldn't learn her lesson. Theo was able to use this logic on both Cliff and Clair (the latter to Cliff's logic) to get out of cleaning the kitchen.
Score another one for Theo in that he didn't even have to explain his logic to Clair as she declared that it was Rudy's responsibility to clean it up once she was convinced Rudy had made the mess. Cliff's expression is golden.
This episode also marks the first use of the Running Gag where Peter runs out of the house as fast as he can should something go wrong.
Cliff's over-the-top description of the car that Denise wanted to buy.
From earlier that same episode, there's the entire scene where Cliff tells an older couple that they're going to have another child... when they already have a 5-year old grandson!
Theo realizing he hugged his teacher after doing well on a very hard test.
Cliff follows it up by faking Clair out in telling her Theo got a 68 on the test (he got an 89).
The entire family discussion in "Denise's Friend" where, among other things, they enact a trust scenario where Theo gets pregnant, Vanessa is seeing a much older guy, and Denise spent the night with a guy. Clair doesn't get angry. She gets mad!
Followed up by Cliff calling "Mom" to "confess" about a time when he and Clair were "very teenagery" before they got married. He actually called Clair's mother.
That scene wasn't even in the original script for the episode. In director Jay Sandrich's commentary, he mentions that the episode was originally supposed to end with Theo's joke after the discussion, but the episode ended up being too short.
Cliff being taken out by Denise and Vanessa while trying to break up the two of them fighting.
"This is Dr. Huxtable! I delivered some of you! I'm a parent, and a taxpayer! I'm also the only adult who will sue little children!" The kids pelt him with snowballs anyway, so he retaliates with his own snowballs and garbage-lid shield.
In "Theo's Holiday", Theo comes home from a sleepover to find that his entire family gives him a taste of the real world. Clair plays some very clever roles, and Theo even gets Cockroach to play his boss.
Dr. Foster. Just, Dr. Foster.
"My father always used to tell me that no matter how stupid the dealer looks, you must always cut the cards."
While Cliff and Clair clean up after Vanessa's Halloween party, they pretend to be two teenagers who have crushes on each other but are too shy to talk to each other, so they have Rudy repeat increasingly-complicated messages between them until she just gets fed up and drags the two of them together for a dance.
Theo hints at wanting to visit Nairobi as his high school graduation present, but Cliff turns it down because he says that he and Clair had already bought him a tie. We don't see Theo's reaction, but the way Cliff laughs at getting him says enough.
Clair's panicking over the fact that a snake is in the house.
When Cliff (who is a VERY impulsive shopper) goes to an appliance store, Clair calls ahead to make sure Cliff is only allowed to buy what he said he would. When Cliff returns he later tells the story of the "man with a very wicked wife who called the store, so he went to another store and charged everything to his wife's credit card."
Sondra and Elvin get engaged and the family plans to use the news to prank Cliff, but he finds out and reverses it on them. At the end, Elvin still one-ups him with a simple joy buzzer.
The entirety of the episode where Cliff takes Theo to the car dealership. The whole thing is a testament to Cosby's comedic timing, made even funnier by the hilarious dialogue between Cosby, Sinbad, and Gilbert Gottfried.
It should be noticed that this same episode had the highest viewership in the run of the whole series.
Cliff and his best friend from the Navy, Scott Kelly, continually one-upping each other by exaggerating the accomplishments of their children. Made double by the fact that Scott was played by Robert Culp, Cosby's longtime close friend and co-star in I Spy.
From the same episode, bald Cockroach and Vanessa's reaction.
In "Golden Anniversary," Theo displays a brilliant lip-synch to James Brown's "I Got the Feelin'" while Cliff, Sondra, Denise and Vanessa act as musicians.
Rudy's very short and to-the-point anti-smoking message, "Smoking is bad for you: It makes your breath stink, your lungs dirty, and then you die!"
Elvin's imitation of Cliff.
Sondra and Elvin declaring they're giving up careers in law and medicine to run a wilderness store and Cliff and Clair's reaction.
Clair: "What do you mean you decided not to go to law school?! Sondra, you have always wanted to go to law school! You never talked about anything else!"
Sondra: "Well, I changed my mind."
Clair: "''Change it back!'"
Of all people, Clair is the one to sneak a too-early taste of Cliff's extremely hot chili. The entire scene is virtually dialogue-free as Cliff easily figures out what happened and gets her a glass of water.
The sad but hilarious disaster that is Theo's prom night.
"Lay-deee! The 3rd grade class is proud to present its musical rendition of Twinkle, Twinkle, Little Star! May God have mercy on us."
In "Theogate," Theo is not telling the whole truth to his family about being late for Vanessa's recital, and after Theo says he wants to be treated like an adult, the family stages a courtroom setting to get the truth out of him.
In "Gone Fishin", Theo discovers a dead gangster while fishing and is interviewed about it. Theo lets his "fame" go to his head and orders everyone he knows to watch the news that night so they can see him on TV. His interview was very long and showboaty, but his appearance on TV was cut to a few seconds because the reporters thought that Rudy and Kenny's discovery of a bird's nest was more interesting, turning him into a laughingstock.
Cliff proving to Denise that he's more than willing to take the money she's offered him when she thought otherwise.
The single most ironic line in the entire series: Cliff telling Rudy that he is not a professional comedian. Of course the audience didn't let Bill get away with that one easily.
Cliff successfully convinces Rudy that "it" is a euphemism for homework instead of sex.
Rudy's friend immediately figuring out that her hamster died while in Rudy's care and they attempted to replace it. Notably this is the fifth time that such as thing happened to her.
In that same episode: the interaction between a sea lion and its trainer while in a vet's waiting room.
Cliff making Rudy and Vanessa live in the basement after they cause structural damage to the house with their fighting.
In one episode, Vanessa is begging Rudy to cover for her in her lies about why she's going out past curfew and explains how much her boyfriend means to her and how they need to see each other. Rudy's response is a perfectly timed, "So?"
Cliff and Olivia's discussion about where babies come from.
Theo calling out both Cliff and Clair about how they never truly support him right before he learns about his dyslexia.
Theo: "Icarus' father didn't support him, either! He just let his wax wings melt and let him fall into the ocean!"
Later in the episode Vanessa reminding her parents of all the times they punished Theo for failing at school when it was probably his dyslexia holding him back.
The entirety of the episode The Day the Spores Landed which can be summed up as thus: The men get pregnant, Hilarity Ensues.
Elvin and Sondra's redneck neighbor Bob is only in one episode, but fully expect to never be able to forget him.
Clair definitely considers a practical joke played on Cliff by Olivia one. Olivia simply put tissues in her shoes to make it look like she's grown several inches overnight and Clair can't stop laughing for the rest of the scene.
Rudy's teacher, Mrs. McGee, gives Cliff detention in her classroom and has him write "I will not do my daughter's homework for her," on the blackboard 100 times.
Funny enough on it's own, but Cliff cranks it Up to Eleven first by writing the sentences in giant letters, then when Mrs. McGee tells him "Don't write big" he switches to teeny-tiny print.
She has a very hard time keeping a straight face during that, which only adds to the hilarity.
Mrs. McGee herself has at least one in every episode she appears in.
Howard "Sandman" Sims challenges Cliff at tap-dancing. Hilarity Ensues for a good five minutes.
Cliff winning the "King of Romance" contest.
Clair, getting ready to tear Vanessa a new one, accidentally slamming the front door in Cliff's face.
While Clair is tearing Vanessa a new one, Rudy sits on the top of the stairs to watch. Clair, not turning around, angrily tells Rudy to go to bed.
Clair's verbal tear-down alternates between hilarious and frightening as she is bonkers with rage. "DON'T YOU DARE OPEN YOUR MOUTH WHEN I'M ASKING YOU A QUESTION!"
Every time Cliff came in from the rain/was forced to go back out into the rain during the Thanksgiving episode.
From the same episode, the giant salad brought by Elvin's parents for the dinner.
Clair: How did you get it in the car?
Elvin: We didn't; we strapped it to the roof.
Cliff's method for sneaking a piece of the cake Clair baked for Martin's parents? Cutting a piece out of the middle, then stuffing the empty space with paper towels and covering it up with icing.
Denise, Clair and Martin's mother all ganging up on Martin for being the cause of Denise believing that her mother-in-law couldn't stand her.
Olivia proving Denise wrong about crying all day if she's left at preschool alone.
Cliff attempting to bid for Night in Tunisia at an auction. He loses, but felt that he ramped up the price so much that the "fool" who won had to pay several thousand dollars. Of course, he later learns who it really was.
Clair: "Ever danced with a fool?"
Pam succumbs to her friends' peer pressure to break curfew on her first night living at the Huxtable house, but gets caught on her way out the door. When they talk about punishments Cliff asks, "Did Rudy tell you about that machine in the basement?"
Poor Rudy begins her first menstrual cycle at the worst possible time.
Rudy: "There we were in English class, talking about punctuation, and I was having my period."
Cliff and Dr. Harmon are brutally defeated at pinochle by the two people who know how to read their every move: their wives.
Followed up with Cliff and Clair returning to the house to find it "booby trapped" by Rudy and Olivia after the two had been watching horror movies and gotten scared.
Rudy and Olivia prank Clair by making it look like Olivia knows all of the answers to a game show.
They try it on Cliff but it backfires when Olivia tells him that Harry S. Truman defeated "ThomasEDeweyTellHimWhatHeWon Frank" in the 1948 election.
Theo, Vanessa and Pam's reactions to learning Clair is beginning menopause and Claire's prank on them.
Pam's second boyfriend, Aaron, is on the Adorkable side and tends to say things that are perfectly normal for him, sound weird to the other people in the room, and hilarious to the audience. The primary example is when he tells Pam how he figured she must have a wonderful digestive system when he was watching her eat an apple.
Cliff explaining to Rudy (during her nightmare) how she got her name.
Cliff: "You are just so rude. In fact, that's how you got your name: Rude-y! Rude-y!"
Vanessa tells the story (of the Rescue Romance variety) wherein she met Dabnis after he saved her from being trapped in an elevator. Sondra reminds her that she lives on the second floor.
"Ohayo." "New Jersey!"
Four words: "I will Hooverize you!" Plus various other puns involving a dustbuster. Elvin even follows it up with, "Assault with a cleanly weapon."
The "Lookback Special" heavily implies that Bill Cosby ad-libbed that entire sequence.
Cliff is cooking a french bread pizza and does everything he can to Troll one of Olivia's friends who clearly wants it, complete with giving him a good whiff of the scent and then ushering him out the door.
Cloud Cuckoo Lander Mrs. Minnifield, whose antics continually lead Cliff to question why he even went to medical school.
Cliff accidentally knocks over the grandfather clock. His first words, "I'm not afraid of Mrs. Huxtable."
After Clair is given her own room to use however she wants, Cliff and the kids figure she's using it to get some serious work done. Cut to Clair making snow angels in the carpet, cutting loose with fast-paced dancing, and ordering Chinese food for delivery with the express instructions that the deliveryman not be followed.
In general, if Bill Cosby knew that a take was falling apart, he would do everything he could to turn the funny Up to Eleven.
When setting up a chess board, Bill is told to "take the black pieces off." To spite the director, he puts the white pieces away instead.
"This is my son, Malcolm. His name is Theo."
Bill was usually the cause of takes falling apart, but even he couldn't hold it in during several takes of, "Is that all you wanted to ask me, Dostor Husstable?"
Bill would constantly tease Phylicia about her baby stomach and what the writers resorted to during season 3's Hide Your Pregnancy.
Bill also had a lot of fun teasing Phylicia after she got married to Ahmad Rashad, especially during rehearsal.
Phylicia: We could snuggle up and read Macbeth and it could take all night.
In one outtake, Bill actually blamed Ahmad for ruining his show because Phylicia "just didn't kiss the same since she got married."
As Phylicia describes, "Even a simple thing like a light bulb would inspire Bill to supreme silliness." Cue a scene where Bill uses the cover of a sneeze to slip a tiny light bulb into his nose and act like it's a giant ball of snot that he pretends to be unaware of for several moments. The audience completely loses it.