Beating X, the deck destruction expert, by decking him out. Also, when he did this, Judai had zero cards left in his deck.
Judai vs. Yugi in the final two episodes of GX. They match each other move for move throughout the entire duel, and in the end Judai loses, but he loses with style, choosing to attack Osiris with Neos even though he knows he'll lose because of it. He got back his joy of dueling with that and he earned it. He even managed to summon both Magma Neos and Shining Flare Wingman in the last turn, both his ace monsters that symbolize the Elemental Hero and Neo Spacian Counterparts of his deck, even Yugi was in complete amazement.
His duel against Pegasus' rogue employee and a copy of The Winged Dragon of Ra.
The end of the duel in Episode 1, Judai pulling Flame Wingman and Skyscraper to own a monster with the same ATK points as Blue-Eyes White Dragon. Plus you can't say Flame Wingman didn't look sweet atop Skyscraper.
And let's not forget the callback to it when he and Chronos rematched near the series' end.
In Johan's duel against Giese Hunt, Johan is about to make the final attack when Giese threatens to tear up a Jerry Beans Man card that he stole from a kid. Judai dives from the ceiling, dropkicks the bastard, and confiscates the card, giving Johan the all clear to finish him off.
Jaden's duel with the Shadow Duellist/Titan (the series's 1st Shadow Game). In his last turn of that duel, he went from having 100LP to his opponent's 1400, 1 card in his hand and no cards on the field, and facing a monster with 2500 ATK points, not to mention a Continuous Trap Card that would wipe out his remaining LP as soon as his opponent's next turn began, to winning the duel. That was pretty awesome in my opinion.
The climax of the Jaden/Yubel duel, in which he "defeats" Yubel with an act of pure, selfless love.
The rematch with Sartorius in Season 4. Jaden couldn't summon monsters on his turn due to a continuous combo. As soon as Jaden destroys it (which earns itself a CMOA by itself), Sartorius preps his field with an indestructible monster with 4000ATK being savy that Jaden will fusion summon his next turn. Jaden beats it with Elemental HERO Magma Neos and wins the duel playing the same card he beat Sartorius the first time with.
Whenever Jaden uses a triple contact fusion.
Summoning Magma Neos which defeats Vennominaga and wins Jaden the duel against Cobra. The animation sequence of the 3 monsters required for this fusion merging together was also very well done with the art making them appear as Badass as possible.
Summoning Storm Neos that can destroy all spells and traps, which ended up freeing the Crystal Beasts from Yubel.
Neos Wisemen, the fusion monster created by fusing Neos and Yubel. Judai even uses Super Fusion (the card he was terrified of the previous season) without a thought to save Yubel from Darkness, and even discarded Winged Kuriboh as a cost, which means Neos Wisemen is the creation of all 3 of Judai's main spirit monsters.
When Darkness destroys Neos Wisemen, Yubel has to leave Judai on his own for the rest of the duel. Judai believing in his deck summons God Neos, the ultimate Neos fusion monster created with a contact fusion of all the Neo Spacians. God Neos destroys a 4000 atk point monster dealing 4000 points of battle damage as well, winning the duel against Darkness.
Jun Manjyome/ Chazz Princeton
Passing his Secret Test of Character at North Academia and learning to value himself based on what he does, not because of his money or family name, is the dividing point when his character went from being a Draco Malfoy Expy to awesome.
Don't forget that he went on to defeat both his brother, who was using a bunch of high powered monsters and forcing Manjyome to use 0-ATK ones...
...And Edo Phoenix, who as a pro duelist shouldn't even be on the same level.
Let's not even get started on the manga, where he beats Judai.
Chazz somehow conjuring up lightning whenever he yells his Catch Phrase.
O'Brien simply walking away after playing his last card of his duel against the Mask of Laughter. No one in either it or the original anime ever did that, which came to a shock for this editor when it happened here. The fact that Mask of Laughter had to read the card's effect himself to realize that he had lost makes the scene even sweeter. For those who never got to see the scene (which is both a CMoA and a Crowning Moment of Funny) in question:
The whole of Hell Kaiser's final duel against the Yubel-possessed Johan. Especially right at the end, when he destroys his own Cyber End Dragon, then re-summons it using Cybernetic Zone, but this time with sixteen thousand attack points. Pity he lost due to the effects of Power Bond right after summoning it.
The Judai vs Kaiser Ryo duel at the very end of season 1. Or more specifically,the end of that duel. First, Kaiser summons Cyber End Dragon with Power Bond to double it's attack points to 8,000. He then plays Limiter Removal to double it's attack again to 16,000. Once he attacks with it, Judai reveals his Battle Fusion quick play spell that adds his opponent's monster's attack to his own monster's, raising his Shining Flare Wingman's attack to 20,900. Kaiser then smiles... and then activates his own copy of Battle Fusion, which raises Cyber End Dragon's attack to 36,900. Judai's response? Activate a trap that causes them both to take damage equal to all the monsters on both sides of the field. The two monsters then clash in an epic explosion.
Judai's insane gambit to activate Elemental Burst.
Even better? This duel held the record for the highest finite number of Attack Points a Monster had for nearly eight years.
During his last duel with Yubel, staring down the monster's Duel Monsters equivalent, Judai finally finds a way to take it down. It seems like he's won, and all that's left to do is mop up Yubel's remaining life points and get the hell out of Dodge. Then comes the three most terrifying words to ever be uttered in the show: "Das...Abschelich...Ritter". Commence pants-filling as Judai realizes Yubel has just gotten started with him.
Dimitri in Episodes 18-19 actually does an excellent job using Yugi's deck, copying Yugi's playstyle very well and pulling off some very impressive moves. Ultimately Jaden won, but only because, in the grand tradition of Yu-Gi-Oh! heroes, he got an Ass Pull in the last few turns to turn the duel around. But the outcome of the duel aside, Dimitri was in control the entire time, bouncing back from everything Jaden threw at him, getting out Yugi's best monsters and whittling Jaden's Life Points down to 800. Hell, he would have won if Jaden's cards followed their real-life rulings.
Hayato gets his time in the sun just before he leaves Duel Academy to be a card designer for Maximillion Pegasus himself. He had to duel Professor Crowler in order to get the school's permission. Chumley, a mediocre duelist at best, got to summon his most powerful creature and power it up with a card he himself designed (Chumley being an exceptional artist), but was countered by Crowler's face-down card and defeated. But Crowler's still impressed with Chumley's performance, and the school allows him to pursue his dream job anyway.
Hell Kaiser vs Sho/Zane vs Syrus. Totally epic duel. Dramatic, emotional, tactical and both players playing brilliantly well. No tedious "one dude is winning the entire duel, then the other guy Ass Pulls victory in the final turn", it was a constant, intense exchange of blows, with Sho/Syrus constantly struggling against Ryo/Zane, but making some good strikes against him and even pulling off 3 or 4 moves that nearly ended the game
Chronos/Crowler, annoying antagonist (sort of) of the first half of Season 1, even gets one when he duels a Shadow Rider/Seven Stars Assassin, keeps the duel going for quite a while, and loses in an exceptionally glorious way as he accepts his defeat like a man while taunting his attacker, even managing to hide in a speech on how Judai/Jaden should always enjoy dueling.
For a very, very, VERY long time Asuka Tenjouin has had to suffer under the title of Faux Action Girl and Informed Ability. But as of her latest duel in the manga, a tag duel alongside Misawa against Amon Garam and Johan Anderson, she has plainly demonstrated that she EARNED her place in Obelisk Blue. step one, activate a trap card to reduce your opponent's monster's attack to zero. Step two, summon a high level monster that prevents your opponent from activating any spells or traps for the rest of the turn, such as MIRROR FORCE! Step three, play a spell card that lets you summon an extra copy of your monster, just to rub it in. Attack, and enjoy. Yeah, Asuka had some help from Misawa, but this victory was hers, no two ways about it.
Professor Midori Hibiki from the manga is reputed to be a better duelist then her younger, world champion brother. When we do get to see her duel, it is awe-inspiring; she freaking snaps her fingers to activate her traps! Unfortunately, her opponent springs the Sadistic Choice on her, but that does not diminish the awesome of her duel at all.
When Chronos summons three Ancient Gear Golems in one turn, then brings out Ancient Gear Ultimate Golem.
After Manjyome defeats Judai at the end of the tournament in the manga, he claims his reward: a duel against Kaiser Ryo, one of the two legendary duelists from the Academia. Who curb stomps him, without taking a single point of damage, after Manjyome got his three strongest cards on the field at the same time. Nobody messes with the Kaiser.
Despite his status as the Creator's Pet, Johan still gets an undeniably awesome moment in his first duel: He uses Ruby's effect to bring out every last one of his crystal beasts to kick Jaden's ass. Granted Jaden still wins but it's an undoubtedly cool moment.
The series's first ED theme is a CMoA on its own: "Genkai Battle" is performed by JAM PROJECT, the most HOT-BLOODEDLY AWESOME J-Pop/Rock band ever, known for providing the assorted theme songs of Super Robot Wars.
Amon gets one when he breaks into Professor Cobra's lab. Instead of the usual fight of children's card games, Cobra tries to use force to get Amon out of his way..... only for Amon to block him and then take off his shirt, showing a massive amount of muscle and leading to hand to hand combat with Cobra. The fact Amon holds his own against a trained soldier makes it all the sweeter.
Amon's Batman Gambit also qualifies: When Cobra figures out Amon is on to him and hasn't participated in a single survival duel, Cobra threatens to expel Amon from the academy, bringing a major scandal to his family in the process. Amon then finds out the truth about the Des Band and decides to turn the scheme back on Cobra by hosting a "Duels for Jewels Tournament" and inviting all of Ra Yellow and Obelisk Blue.Cobra had just turned the Des Bands Up to Eleven, amplifying their exhaustion effects. Amon is banking on Cobra not risking so many people at once. The look on Cobra's face when he finds out what Amon has done is priceless.
You can't forget Sho/Syrus' duel against the Psycho-style user, after merging his deck with that of his brother, Kaiser Ryo's, he proceeds to duel against someone that would have beaten his brother, only to pull out a card designed to perfectly take advantage of Cyberdark Dragon's effect and be able to bypass the card preventing dragon monsters from being sent to the graveyard, and Sho finally steps out of his brothers shadow with 3 words, Full Darkness Burst!
The final match between Crowler and Jaden was a hell of a fight, both emotionally and strategically.
In season 3 when Zane and Aster play a Mook Horror Show on two of the Supreme King's goblin henchmen.
Both goblins: I told you all I know... have mercy just let me go!
Zane: Of course but first I need to finish what I started and...
Aster: ...turn you into star dust.
Speaking of Aster Phoenix... his duels involving his Destiny Hero cards involve some really awesome moments.
The first time he duels with the Destiny Heroes against Jaden, he effectively was able to control time and counter every strategy Jaden attempted.
Aster's duel against Adrian. Adrian summons Exodius, a generic haxed monster without weakness, and Aster's strategy consists of several combos utilizing his Destiny Heroes to stall and inflict damage to Adrian's life points. Aster would have won had Adrian not played some random card conveniently negating Aster's last stall effect.