Episode 10 was the first real CMoA for Heero: when his sole reason for fighting was threatened if he doesn't surrender, his superior announced that they do surrender but they won't hand over the Gundam. Heero pulled out a self-destruct switch, whispered "Mission accepted" and promptly blew himself up. And he survived the explosion without any lasting injuries (so did his Gundam, for that matter).
To some extent, Quatre had one when he actually piloted Wing Zero without the Zero System driving him permanently insane. He's one of only three pilots who ever managed that stunt but even he was sufficiently intimidated by it that he never sat in the cockpit again.
Unlike Heero who routinely does it because he has so much emotional self-control that the Zero System simply can't use anything to Mind Rape him.
Relena's first Crowning Moment came in the school ball episode. Heero has her at gunpoint at school, but Relena doesn't blink and basically tells him: "You'd like to kill me, Heero? Try it. But let me warn you, it would be stupid to do so when everyone's at school and enjoying themselves... Shall we dance, instead?" She utterly and completely pwns him and even ropes the cold assassin into dancing with her. That requires balls, er, boobs.
The scene of Zechs reappearance after his assumed death. "Zechs Marquise?! I thought you were dead!" "That's right, I was. But I found that I cannot quietly sleep in my grave, while Treize's spirit is still roaming among us."
The Series has more CMoA than can possily be listed, but of particular note is the final episode when Heero fires his BFG at the giant space fortress hurtling towards earth as he begins to burn in the upper atmosphere while yelling "I will... I will... I will survive!" Not to mention when he appears moments later flying away from the massive blast in his jet mode in ultra dramatic style. This is amazingly awesome because of the fact he pretty much screams it (at least in Japanese); this is coming from a guy who has never raised his voice prior. To top it off, for the majority of the show he didn't care whether he lived or died as long as his mission was completed. Watching that scene was so... squee.
Fan-favorite Duo Maxwell finally got his own CMOA late in the series when he was faced with two Gundam-class machines, each using AI based on his friends Heero and Trowa. He takes both of them down at the same time with little effort, pausing only to coolly comment "Maybe next time you should use my data."
Also in the final arc of the series, there's a scene where Trowa is infiltrating the space fortress Libra. A pair of enemy soldiers emerge from a nearby hallway and start shooting at him. Trowa performs an incredible acrobatic jump, landing on a high catwalk a distance away...and then bows to the guys who just tried to kill him before running off.
The entire setup of the Antarctica duel: Zechs is mad that OZ messed up his fair fight with Heero, so he defies orders to secretly rebuild the Gundam, has Noin locate the pilot, then brings him to a secluded base just so they can have their one-on-one uninterrupted. The fight itself is decently cool, but the real CMoA comes when OZ, having discovered Zechs' treachery, sends literally hundreds of mobile suits to capture everyone at the base. In order to buy time for everyone (including Heero, Trowa, and Relena) to get away safely, he charges the entire OZ fleet solo, crying "Glory to the colonies!"
The end of episode 41 is undeniably one of the high points of the series. Two moments stand out: post-amnesia Trowa saving Noin's ass and Zechs destroying the entire Barge station with Epyon's beam saber after the rest of his attack force has been wiped out.
Bonus points for the English VA work: you can hear the sheer venom in Zech's voice as he takes down Barge.
Zechs:You're not needed here.We have no need for you in outer space!
Quatre's CMOA comes in the series when he goes after the maddened Trowa who's using the Wing Zero and is driven mad by the Zero System. He knows too horrifyingly well the effects of the System, yet he doesn't hesitate to try de-brainwashing Trowa before he blows up the colony he wants to protect. And he succeeds.
He gets another late in the series when he manages to master the ZERO System on only his second usage of it AND gets the other Gundam Pilots to drop their "I work alone" attitudes in order to execute precision strategies, thwarting Dorothy and White Fang's own use of the System. Heero may be the protagonist, but Quatre is hands-down the Wing Team's leader.
A scene not too long after Quatre and Heero escape to Earth after Quatre's Sanity Slippage and Quatre holds up several men at gunpoint with a machine gun. Sure it's small and somewhat pointless, but considering Quatre is considered weaker than the other pilots, he's still pressuring the soldiers to surrender while holding a machine gun.
Weaker? The same several episodes show Quatre supporting Heero several times, up to and including snapping the other pilot out of his own Zero Sanity Slippage, piloting a (stolen) jet, taking over an entire battleship without any casualties and culminating in him pushing Heero into going to Sanc which is where they're needed. Physically weaker perhaps, but from this point and onwards pretty much every moment is a CMOA of Quatre's abilities as a soldier and a leader.
Which is then flipped on its head when Treize reveals during his duel with Wufei, who accuses him of being heartless, giving him a Shut Up, Hannibal! by counting off the names of everyone who ever died for him. Seconds later he jumps Wufei, only to be fatally stabbed. Cue Tear Jerker moment as Wufei gives a manly cry "I didn't think I'd win..."
Trowa uses the traveling circus act as a disguise to hide his Gundam, and reveals it during the show at a military base. Where he proceeds to destroy everything. Just as he is about to commit suicide with his Self-Destruct Mechanism, his sister slaps him out of it.
Watching Mooks scream out "IT'S A GUNDAM!!" is both awesome and funny at the same time. The most notable example is the Deathscythe Hell's first battle where it proceeds to scare an OZ pilot shitless before wreaking havoc on all the others.
"The God of Death is back from Hell!"
Lady Une freeing the Gundam pilots as well as her final speech have to count.
Lady Une pulls an Awesome moment early in the series. After General Septum gives his speech, Une tells him "... we won't be needing you any further." Then the floor under Septum drops open , causing him to fall out of the airplane. Une smirks, then swipes out a pistol - and shoots the falling Septum in the head. A moment so awesome, the Toonami trailer used it.
For for a OZ pilot, Walker deserves mention. After providing Zechs with Tallgeese, Walker goes into battle to buy him some time and gather data on the Gundams. He saves an Alliance general and surrounds Heavyarms with his troops. However, Quatre and the Magnac Corps show up, shooting up the Aries. Utterly outnumbered and outmatched, Walker charges at Sandrock, shouting "Come get me, you monster!" Quatre catches the Aries in his heat shotels. As his mobile suit is being crushed, Walker calmly muses "Well, I always wanted to know how much this thing can take" before he dies. Not bad for a guy with one name.
Heero in Endless Waltz having finally arrived, with Wing Zero, at the compound where Relena and Mariemaia are:
Heero: Let me confirm: your shelter shields are activated?
Not to mention Relena intercepting Lady Une's Armor-Piercing Slap for Mariemaia and delivering one herself.
At the English-language premiere of Endless Waltz at Anime Weekend Atlanta, the entire crowd burst into applause at both these moments.
A retroactive moment for Trieze; even after he has been dead a full year, just sharing his name is almost enough to allow Mariemaia and Dekim Barton to conquer the world. The only reason it doesn't work is because Trieze's soldiers are so loyal to his vision that when Dekim oversteps that vision they kill him. How many characters can claim to nearly take over the world from beyond the grave?
In one episode, a group of former OZ soldiers have taken a colony, including Catherine Bloom, hostage. Quatre and Trowa are outside, with Quatre having just talked Trowa down from Zero System induced madness, and the leader of the OZ group orders that Taurus Mobile Dolls be positioned around every one of the colony's entrance points to intercept them. The orders have barely left his mouth when a Taurus falls apart. Cue several Taurus Mobile Dolls falling to bits, and then Deathscythe Hell emerging from the smoke. Duo, holding the edge of his beam scythe to the OZ soldiers, who don't even have the benefit of being in mobile suits, notes that he's very good at getting in and out of places unnoticed. Which is saying something, given he's in a giant robot.
Dorothy gets an understated moment when Quinze sends a legion of Virgo Mobile Dolls to attack the Gundam pilots in Peacemillion. She predicts a total loss for the White Fang. Quinze chastises her for trying to give him orders, stating that this is not some kid's game. When the Gundams proceed to mop up every last one of the Virgos, Dorothy calmly notes that it was precisely the outcome she'd predicted, leaving the bridge, while Quinze just shudders in disbelief and terror at what he's just witnessed.