Considering The Godfather is both critically acclaimed AND popularly beloved, the entire movie could be one long Crowning Moment. The acting is so good that otherwise tragic scenes are memorable for the delivery of the actors alone.
Considering that the second film is often cited as superior, it also counts.
Moe Greene's rant at being disrespected by Michael in Las Vegas. "Son of a bitch, do you know who I am? I'm Moe Greene! I made my bones when you were going out with cheerleaders!"
At the hospital, when Michael realizes his father is getting set up for another hit, he's forced to improvise with little help until Enzo the Baker shows up paying his respects for Don Vito. Enzo offers willingly to help Michael ("For your father"), and Michael gets Enzo to stand with him in front of the hospital as a bluff to scare off the incoming assassins. Once the car of hitmen drive off, Enzo tries to light up a cigarette but can't because his hands are shaking too much. Michael helps with the lighter, and notices with some awe that his own hands aren't trembling.
Remember that Enzo also was a soldier. He was in the Italian army and got captured and sent to America to help the war effort. He must have experienced combat as well but still wasn't as calm as Michael. So it's a double moment of Awesome for the both of them - Michael was able to do it with nerves of steel, and Enzo kept on even though he was scared out of his wits.
The murders of Solozzo and Captain McCluskey by Michael, sending the formerly squeaky clean war hero down the same criminal path as the rest of his family. It was such a Crowning Moment that it convinced Paramount, who had been looking for any reason to fire Francis Ford Coppola (and Al Pacino) and get another director, that he might actually know what he was doing.
The apologetic way Neri closes the door between Michael and Kay as Michael receives Clemenza and other mafia lieutenants. It makes Kay realize Michael just lied to her about the Family business. But it's also the best way to end the film.
It's bad news for the horse, but the way the Corleones handle the corrupt movie producer (and pedophile) Woltz by discreetly placing the head of Woltz's prized race horse Karthoum in Woltz's bed. The fact the mobsters were capable of doing such an act quietly and efficiently demonstrates some serious skills. Not to mention how far they were willing to go to punish Woltz.
Tom Hagen gets an understated moment shortly before that. Woltz, explaining why he doesn't want Johnny Fontaine in his new film, breaks down into a violent rant and angrily demands Tom get out. Hagen calmly sets down his utensils, stands up, and quietly thanks Woltz for the pleasant tour of his home (which it had been, up until that point), and says his farewells without once losing his cool. Even before the scene with the horse, you know he's gotten the upper hand.
The last 15 minutes or so of The Godfather are pure awesome for Michael Corleone. The Corleone Family is at its lowest moment; Sonny and Michael's first wife murdered, Vito almost murdered, the Family forced to accept a truce with the people who did it, and their rivals moving in on their business interests. While he's standing as godfather to his sister's baby, Michael calmly says yes to his vows while, at the exact same moment, his men all over the city and the country are pulling off a series of assassinations on every opposing mob leader or power broker that stand in his way, reestablishing the Corleones as the most powerful crime family in the nation and sending the message that Michael is even more cunning and ruthless than his father. Then he goes up to his brother-in-law Carlo, whose baby he was just named godfather for, and tells him that he knows that Carlo was involved in the death of Michael's older brother and a conspiracy against Michael's family. He pretends he's putting Carlo on a bus, but actually sends him off to be killed. And then he calmly denies it when his hysterical sister accuses him of doing this and uses every ounce of his wife's trust to tell her a stone cold lie and make her believe he had nothing to do with it, if only briefly.
New Year's Day in Havana, Michael at a celebration with his brother Fredo, the brother who secretly (and unintentionally) nearly had him assassinated. In the middle of the roaring party, Michael whispers some travel arrangements in Fredo's ear, then delivers the Kiss of Death to him full on the lips and grabs him without letting go. "I know it was you, Fredo. You broke my heart. You broke my heart."
Michael's confrontation with Fredo back in Nevada after they fled from Cuba. With Fredo expressing all of the rage and frustration of being passed over and belittled by his little brother. For John Cazale, this is his finest moment as an actor.
Taken care of me?! You're my kid brother, and you take care of me?! Did you ever think about that? Huh? Did you ever once think about that?! Send Fredo off to do this, send Fredo off to do that! Let Fredo take care of some Mickey Mouse nightclub somewhere! Send Fredo to pick somebody up at the airport! I'm your older brother, Mike, and I was stepped over!
The whole story of Vito Corleone's rise to becoming the Godfather is basically just one Crowning Moment of Awesome after another, culminating in this line: "My father's name was Antonio Andolini...and this is for you!"
Linked to that, the deleted scenes from the Saga that show Vito tracking down Don Ciccio's mooks and killing them as well.
An understated one from Vito's wife Carmela, who while never asking about his business, knows he can help her friend Signora Columbo who is being evicted from her home.
Hyman Roth's pep speech to Michael while in Cuba, waiting on their deal with the corrupt government to go through.
"Michael, we're bigger than US Steel."
Hyman Roth's legendary "Moe Green" speech. Many found themselves rooting for him after that part.
The final flashback of Part II on Vito's birthday day and after Pearl Harbor. In just a few minutes it manages to summarize and flesh out the traits of many posthumous and still young or not fully developed characters back then. Special mention to Sonny's role, who takes over several Vito's lines form the novel after Brando made a no-show. Vito, who is about to arrive still manages to haunt the scene being a literal looming ghost, as even in absentia he dominates the conversation.
Michael gets another when Tom Hagen tells him they have no way of getting to Hyman Roth.
Michael: Tom, I'm surprised at you. If there's one thing that's certain in this world, if there's one thing history has taught us, it is that you can kill anybody.
Sonny's bastard Vincent Mancini shows he's his father's son by expertly taking out two goons sent by Joey Zaza to kill him in his apartment.
The mass assassination of the Commission by Joey Zaza and Don Abetello: almost a Serial Escalation from the infamous Baptism massacre from Part I where a helicopter is brought in outside the meeting room and military firepower gets unleashed on the entire Mafia leadership. One critic noted it was "an unholy matrimony" of the Godfather series to Coppola's other epic work Apocalypse Now.
Michael's Passing the Torch moment to Vincent is a truly awesome piece of cinematography, mainly because of how quiet and understated it is. It begins with Michael gently trying to dissuade Vincent, telling him that being a Mafia Don isn't all power and glamour. And when it's clear that Vincent genuinely wants it, he calls his lieutenants in to witness, and declares, "From this moment on, call yourself Vincenzo Corleone." Cue the kissing of hands and theme music.
Despite being used to punctuate a tragic ending, "Cavalleria Rusticana" is a piece so powerful that at times it raises about the drama.
Mosca the assassin is obviously getting on in years but it doesn't stop him from being frighteningly competent at his job. In the finale, he cuts a swathe through much younger and fitter Corleone bodyguards with nobody in the opera building being the wiser, and comes within a hair's breadth of killing Michael himself.