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Inuyasha gets his first one when he first uses the Tessaiga and cuts Sesshomaru's arm off.
Maybe I'm not so worthless then, AM I?! He wounds Sesshomaru in a way that the older brother never thought possible, and then told him that both of them were nothing compared to their father, with Inu-daddy having granted the sword to Inuyasha, meaning that Sesshomaru was never meant to have it.
The first time Inuyasha transforms from human to half-demon. A surprisingly heroic application of glowing red eyes.
Inuyasha vs Ryukotsusei. He defeated a giant dragon (who even his father hadn't been able to defeat) by cutting it up with the newly mastered Backlash Wave! You got to respect that
Anytime Inu Yasha and Sesshoumaru get within a mile of each other, at least one of them is going to get a CMoA, but when they are also near Mouryoumaru, they practically chain them together, such as human Inu Yasha taking advantage of Sesshoumaru's pride-based Beam Spam outburst against a youki-absorbing Mouryoumaru by preventing his allies from saving him before sunrise so that the otherwise lethal absorbing of his returning youki would just overload the little bastard instead.
And from the final battle, Inu Yasha cutting a hole through TIME AND SPACE to fight inside the Shikon No Tama after it had transported itself and Kagome back to Kagome's time and then doing it AGAIN when he's got a moment's respite from days of fighting the evil half of the Shikon no Tama's spirit to go to the pocket dimension that Kagome was located in and keep her from falling all the way into the despair of solitude.
In one episode, the entire group minus Inuyasha were cocooned alive, and being transformed into youkai moths. While the transformations are happening, they're experiencing their worst nightmares: Miroku being sucked alive into his Wind Tunnel, Sango reliving the moment where she was prepared to murder her little brother, Shippou having to face a small army of lizard youkai and the Thunder Brothers who murdered his father, and Kagome seeing Naraku attack her while she's at school in the present. Inuyasha continues to scream at his friends, mostly berating them for letting this happen to them, and his voice penetrates their nightmares, resulting in: Miroku remembering Inuyasha threatening to cut his hand off if he risked himself with the Wind Tunnel again, Sango's memory of Inuyasha stopping her from killing her brother, Shippou being encouraged by Inuyasha and finishing off all his foes, and Kagome watching a human Inuyasha appear and transform into his half-demon form to face Naraku. The entire sequence doubles as a Crowning Moment of Heartwarming.
Kagome Higurashi shooting Naraku with a single arrow, pissed off at him for exploiting Sango's for her brother into stealing Inuyasha's Tessaiga for him, then manipulating her brother Kohaku into almost killing Sango... which is enough to have her use said arrow to purify the heavily poisoned air in her surroundings and blast half of Naraku's body off.
To say nothing of Sesshomaru. In "The Woman Who Loved Sesshomaru", he picks up the Tessaiga (which, being a demon, causes him incredible pain) and throws a Wind Scar at an oncoming demon, one-shotting it. The other regulars were floored.
He does it again in the third movie while fighting Inuyasha, who is possessed by an enormously powerful evil Empathic Weapon - only the first of a series of Awesome Moments for Sesshoumaru throughout the film, one of which involves blocking that evil Empathic Weapon by punching it away with his bare fist.
Sesshoumaru's crowning moment, however, has got to be his storming of Hell to get Rin, his Morality Pet, back, in one of the greatest Papa Wolf moments in the entire manga: When Rin is taken to the underworld by a hellhound, Sesshoumaru follows and kills it. When he finds out she's already dead, he then proceeds to kick the King of Hell's ass to get her back. When this doesn't work, he actually shows the closest thing to human emotion he's ever done in the series, purifies the souls of the dead as an afterthought, then rips a hole back into normal reality. After all of this, his mother (a youkai queen) resurrects Rin since Sesshoumaru, of all people, is clearly unhappy about her death. He goes from Aloof Big Brother to a combination of John Creasy, Jesus, and Spawn in a Crowning Moment of Awesome and Crowning Moment of Heartwarming unparalleled in the other 500+ chapters of the manga. DO. NOT. MESS. WITH. RIN.
Combined with Crowning Moment of Heartwarming, there's Sesshoumaru throwing away Tenseiga out of grief for having failed to save Rin and then taking it back and using it to purify Hell out of pity for the souls trapped there, not to mention his final real battle with Inu Yasha, where he deliberately shatters his Tenseiga on Tessaiga in order to stop Naraku from manipulating it to kill Inu Yasha and give up the Meidou ability to his little brother's sword out of recognition of his worthiness to wield their father's legendary blade.
Sesshomaru's Big Damn Heroes moment where he effortlessly killed Mukotsu by slicing him in half.
Sango, a sixteen year old human girl, physically dug herself out of the grave she was buried alive in.
Miroku, traveling with Sango who has been severely weakened, uses his Wind Tunnel to continuously suck up poisonous bugs to protect her. This causes him ridiculous pain and was probably going to kill him, but just goes to show he was willing to die to save the girl he loved.
Or how about Miroku doing this same thing near the end of the series? Trying to make a Heroic Sacrifice by almost sucking in Naraku's heart with his Wind Tunnel, despite the poisonous insects and massive amounts of miasma. Mostly driven by the desire to eliminate Naraku before he could kill Kohaku by taking his jewel shard, so that Sango would not go through the pain of losing her little brother again, Miroku toughs it out even while bleeding from the mouth, nose, and eyes, and would have killed Naraku had Inuyasha not forcibly closed the Wind Tunnel. Naraku even says that Inuyasha just gave up their best chance of killing him. Its also one of the few times where we see Inuyasha actually concerned about Miroku.
Allowing Tekkei to eat him, only to kill her by bursting the inside of her forehead.
Kagura's intro, where she completely destroys an entire army of wolf demons in just a few strokes of her fan, and not only that, proceeds to make one walk over to Koga and deliver news while dead and then when everyone gets there, uses the army to put on a puppet-show to fool Koga into thinking Inuyasha killed them.
And Kanna, who despite being a little girl, can easily deflect almost everyone elses' attacks, and suck out your soul. She deflects the legendary Wind Scar easily and leaves Inuyasha unconscious in her intro.
Then Kagome gets one when Kanna fails to get all of Kagome's soul because Kanna's mirror filled up. Then a little later Kagome fires a sacred arrow into Kann's mirror, overloading it, and forcing Kanna to dump all of the captured souls to keep her mirror from breaking.
Kikyo convincing Saint Hakushin to let go of his anger and take down the barrier he had around Mount Hakurei. With only kind words and a Cooldown Hug as her "weapons".
Even Kohaku earns one by willingly stepping into Naraku's clutches, in order to jam one of Kagome's arrows, supercharged with Kikyou's light into the shell covering the Shikon no Tama to give the Inu-tachi an opening to attempt to kill him.
In episode 20 of Final Act, Kohaku finally decides to confront Naraku.