In Part II, when Frank Pentangeli wants the band at the Communion reception to play a Tarantella, he tries to sing out the beat for the band who have no clue. They seem to get it right at first, until they turn it into "Pop Goes The Weasel" and Pentangeli gives up in exasperation.
Pretty much everything Clemenza says as he doles out his wisdom to Michael or the others. Even when he's giving orders to have Mooks like Paulie whacked.
Luca Brasi rehearsing a small scripted speech he wrote thanking Don Corleone for inviting him to Connie's wedding. Watching a massive, scary Italian hitman mutter words of thanks over and over is funny enough by itself. But then he flubs the speech once he actually meets with Don Vito. This was part of a Throw It In moment; Lenny Montana had flubbed his line first - terrified of acting opposite legend Marlon Brando - and Coppola liked it so much he kept that version and added the rehearsal scene later.
The fast wit of Jack Woltz as he uses every ethnic slur he can think of when Tom Hagen comes calling about getting a part for Johnny Fontane:
Woltz: Johnny Fontane will never get that movie! I don't care how many dago wop guinea greaseball goombahs come out of the woodwork! Tom Hagen: I'm German-Irish. Woltz: Well, let me tell you something, my kraut mick friend...
His reason for denying the part for Fontane crosses enough lines into macabre humor:
Woltz: You don't understand. Johnny Fontane never gets that movie. That part is perfect for him. It'll make him a big star. I'm gonna run him out of the movies. And let me tell you why! Johnny Fontane ruined one of Woltz International's most valuable proteges. For three years we had her under contract, singing lessons, dancing lessons, acting lessons. I spent hundreds of thousands of dollars. I was gonna make her a big star! And let me be even more frank, just to show you that I'm not a hard-hearted man, that it's not all dollars and cents. She was beautiful, she was innocent, she was the greatest piece of ass I've ever had, and I've had it all over the world! And then Johnny Fontane comes along with his olive oil voice and guinea charm... and she runs off. She threw it all away just to make me look ridiculous! And a man in my position can't afford to be made to look ridiculous!
And then we receive Mood Whiplash once we learn just exactly what is done to his prize horse Khartoum afterwards.
In the novel, Vito's reaction to Woltz's grudge against Johnny was essentially "What an Idiot!" To let base desires interfere with running your business seemed ludicrous to him.
Clemenza's "Leave the gun. Take the cannoli", a partial ad-lib.
In Part II, Vito is now the new local crime lord. Signora Columbo, a widowed friend of his wife, is threatened with eviction because her son's dog's barking is disturbing the neighbors. Vito tries to talk to the landlord Signor Roberto, on the street and offers to pay the woman's rent as long as the dog stays. The landlord angrily refuses and Vito tells him to ask around the neighborhood about him. Later Roberto comes to see Vito at his office, now scared to death after finding out who he is and agrees to let the widow keep the dog. Vito without saying anything also gets Roberto to lower her rent, then pay no rent. The man then can't get out of there fast enough but can't open the door! He tries and tries until Genco, an associate of Vito's unlocks it for him and he hastily leaves. Genco then jokes to Vito that the man will probably move to the Bronx.
One of the few funny things Michael says in the trilogy is this exchange from Part III with his sister Connie, who has now become a sort of consigliere:
Connie: Michael, now they'll fear you. Michael: Maybe they should fear you!
Also in Part III, after the massacre in Atlantic City, Michael keeps trying to figure out who is the real mastermind behind it while his nephew Vincent keeps prodding him to give the order to strike back at Joey Zaza until Michael explodes: "VINCENT WILL YOU SHUT UP!!"
In Part II, the whole sequence of how Clemenza, Vito's neighbour, introduces himself to Vito and suckers him into a life of crime at the same time. Firstly, one night, Clemenza gets Vito's attention across the airshaft of their building by calling to him in a panic and imploring him to mind something, and tosses Vito a bundle wrapped in a blanket; Vito opens it and looks rather perplexed to find that it's a gun. A day or so later, Clemenza calls on Vito and, with enormous dignity, thanks him, and tells Vito that he wants to repay him for his kindness by giving him a rug. Vito, who just wants a quiet life, politely declines, but Clemenza insists, and Vito is once more perplexed to find himself tagging along as Clemenza forces entry to a complete stranger's house and steals a rug, which he presents to Vito afterwards. The best moment is Vito's bemused expression as this total wackjob makes him an accomplice to unlicensed possession of a weapon, breaking & entering, and theft.
In Part III, Michael orders feuding Vincent and Joey Zasa to embrace and "make peace." As they do, Joey calls Vincent a bastard under his breath. Vincent responds by biting off a piece of Zasa's ear. As both men are rushed out of the room, Michael reacts simply with a sigh and a Face Palm, with a look on his face that says "I should've expect that."