The Major has a tendency to become a walking, talking CMOA on a regular basis. A "Crowning Existence of Awesome", if you will.
Episode 23 "Equinox". The Major had posed as the Laughing Man and had an extended conversation with the head of Serano Genomics, the whole time, Serano was convinced she was the genuine article. "And I was never in a single school play either." indeed.
The Major actually has another moment. An earlier episode had a Humongous Mecha chasing her, Batou, and a VIP that had info on the Government Conspiracy. She leads the mech away, and soon gets her ass handed to her, to the point of the mech blowing off her arm and attempting to squish her head into the pavement. Cue the cavalry with their BFG managing to stop the mech cold... then we get to see Motoko get up, take the giant gun, and proceed to unload the rest of the bullets on the fallen mech up close, singlehandedly (literally), all while the pilot is begging for mercy. She doesn't kill him, but a point is made: never piss off The Major. And Aramaki mentioned that the guy was very cooperative afterward... Why? Because the Major scared him shitless once the tables were turned.
This was probably because she — and several other members of Section 9 — replayed Togusa's memories of getting shot by narcs while learning the truth about the Murai Vaccine. Between the breadth of the conspiracy, everyone being influenced by Togusa's hyper-idealistic nature and witnessing Togusa's memories of the narcs slaughtering the Sunflower Society, she and the rest of Section 9 were already pissed off. Kusanagi nearly getting her head smushed by the exact same guy? Oh yeah, she's in full Cool Big Sis mode.
Aramaki gets a good one in the first season when, tied up and armed with nothing and unable to communicate outside the building he's in, he rescues his friend, talks the people who have taken him hostage into switching sides, completely fakes out the corrupt police trying to assassinate him, his friend and the hostage takers, then has the classic Aramaki moment where he confronts the police and has them arrested. Section 9 works for him for a reason.
"Hey! Dumbass at the window! Get on over here!"
"What the hell is with this geezer's tactical competence?"
Ishikawa has a CMOA in the last episode of SAC 2nd Gig, when after one of Gouda's lackeys pulls a gun on him demanding he hand over the plutonium, he knocks the guy out with his left arm, still in a cast.
"Don't screw with us, punk. Section 09 practically invented dirty tricks and information warfare."
What makes the above moment so special is that Ishikawa's forte is Data Gathering, not combat, and that he's usually working behind the scenes. So him doing something a bit more physically kickass instead of mentally is good deal of what makes this moment so utterly awesome.
One for Batou, Section 9's Number 2 Badass (after the Major), is when, rather than his usual kicking physical ass kickass stuff (though he does have a few CMOA that follow along those lines too), he's telling Gouda that he sucks, and why, deconstructing his plan, well, what Section 9 know of it so far. Sure, he was reading keynotes given him by the Major, but still, that scene must have left a massive dent in Gouda's ego.
On one occasion, Batou needed extra processing power and so he used the cyberbrains of the customers at a pachinko parlor he owned, while making the machines pay out big in return for the help.
When, at the end of Stand Alone Complex, Ishikawa releases the data seeds and then catches the Umibozu commandos in an explosion. And nearly walking away from it, then snarking at The Captain while he's being beaten.
The Tachikomas are cute little Crowning Moments on legs. Everything they do ends, eventually, in a Moment of Awesome.
Tachikomas sacrificing themselves for Batou? Three weaponless Tachikomas against a full battle suit. So awesome that it convinced the Major that they'd grown souls. Also qualifies as a Tear Jerker. What's particularly striking is that, when the Tachikomas are on the brink of despair over their powerlessness to stop the armored suit without ammunition, the Major is the one to talk them out of it and inspire them to succeed. She does this by assuring them that their human-like curiosity and ability to experience feeling as people do, the very thing that originally convinced her they had become useless, is more empowering than their weapons would be. This is tantamount to the Major, of all people, admitting she was wrong.
Just to hammer the point home, remember that they are intelligent tanks, designed and built as weapons. They gain sentience and what do they do? Turn against their creators? No. They learn to love and sacrifice their lives of their own free will.
And later, at the end of 2nd Gig, The Tachikomas hacking the thruster controls of their satellite, which contained all their personality data, and ramming it into a nuclear missile. They make this more awesome by singing while doing it. What's even better is that they disobeyed the Major's orders, and came up with the plan on their own.
Both of these were made all the more awesome by the fact that the song was abouthow theywere alive and earlier they had pointed out a song they were singing (as they were being taken off to the labs to be disassembled) was about cattle being taken off to market and how "economic need takes precedence over friendship" without a single hint of bitterness respectively.
During the Ghost In The Shell anime series, Togusa uses more-than-usual force to subdue a cybernetically-enhanced suspect he saw assaulting a woman. Being a cyborg, said suspect had to have several bullets shot into each of his limbs before he stopped. During the trial, Togusa is crucified by the suspect's defense attorney for having a (false) anti-cyborg bias. When it becomes apparent the suspect is going to be let off, Major Motoko Kusanagi, the officer's superior, blackmails them into ending the trial with a guilty verdict. She does this by hacking into Togusa's body and pretending he's going to quit the force and go to the press with "secrets". And yes, she does this in the middle of court.
Togusa's CMOA came near the end of the first season when he risks his life, and actually gets shot, finding a critical piece of evidence that (arguably) led to the solving of the Laughing Man case. What makes this particularly badass is the fact that you have to consider that he is one of the few members of Section 9 who doesn't have a large number of prosthetics, and the only one without military training. In other words, he was about ten times as vulnerable in this situation as anyone else on the team would have been, and his biggest concern was to just get the necessary info to the right people. Awesome.
Togusa is pretty much continually awesome in Stand Alone Complex, even compared to the movies in part because of this, but also because he has that "first responder" instinct, rushing into places others are running away from. He's like Murphy in Robocop, except he studiously avoids becoming a cyborg.
The series itself probably has a CMOA when Section 9 uses American Spy Satellites to listen to every single electronic communication in post-cyberpunk Japan in real time.
The Laughing Man is in itself a Crowning Moment of Awesome. At the very least, it's an all-pervasive cultural phenomenon unintentionally started by someone who's possibly the world's most skilled hacker, accidentally inspires thirty-nine simultaneous assassination attempts on the same person and is quite probably a sentient pure-data entity spontaneously spawned by pure injustice. To top it all off, the Laughing Man is specifically stated, in-canon, to be an entity that's too cool to exist. Awesome.
It is never told who, or what, put the information there when Aoi stumbled on it. it can be presumed that, somewhere out there, someone wants to see the justice through just like what Aoi did.
Episode 4 of 2nd Gig, where Section Nine goes up against the rampant AI Jigabachi AV attack chopper and it's standard Jigabachi cousins. The entire scene is full of awesome, from the Tachikomas playing cat and mouse with the Jigabachis missiles and gunfire, to the Major physically restraining an attack helicopter by herself, to Saito pulling off a million to one shot on the Jigabachi AV's cockpit.
Can we just go back and look at this again? The Major gets into a tug-of-war with an artificially-intelligent attack helicopter, loaded for bear and wins.
And the famous scene where the Major kills a guy through a skyscraper window, then fades into the night, while in freefall.
Every. Single. One of them.
That said, if you look at it carefully, what actually happens is that the Major disables the screens and distracts the hostage taker, who moves his head just enough that Saito is able to take the shot. Which is also awesome, because Saito's shooting from a helicopter, which is not going to be as stable as firing from the ground.
The JASDF's epic flyby of the American sub.
One of The Major's girlfriends is a nurse who reports organs being stolen. When Section 9 track down the thieves she and Batou pretend to be Yakuza, chasing after them with Tachikomas and scaring them into confession, before The Major goes after the mastermind with a large knife, threatening to cut him up and sell his body parts on the black market.
Batou single handedly defeating a small group of professional soldiers and a powered armour suit with nothing more than a pistol, one grenade and one eye-hack in episode 24. This man can sure hold his ground.
The opening songs for both seasons of Stand Alone Complex, and the closing songs. Yoko Kanno delivering her usual excellent composition, using a Russian opera style singer for the openings, a very J-pop singing style for the closers, all fitting the show perfectly. Pure beauty.