Let's be honest, the Hulk (even more than the other characters) is a walking CMOA. Seriously, he gets at least one in every episode he's in.
Season 1
Micro-Episodes
Iron Man overcoming a severe power drain and being held at gunpoint by the SHIELD Mandroids in order to defeat the HYDRA Dreadnoughts in the climax of his series of shorts.
Nick Fury. Why is his hair white? Old Age? Yeah, right. No, his hair's white because he got into a fight with Baron Von Strucker who drained his life force, and he decided to walk away is if losing a decent percentage of his life force was worth it to keep this one villain from escaping.
The Grim Reaper. In comic books, a lowly crook who has an arm that can cause a coma and a necromancer. His claim to fame: being Wonder Man's brother. How does he get introduced? Why, he's walking through a SHIELD scanner, and they realize he has an implant. He then turns into a fully fledged ninja, and breaks a high priority prisoner out of a jail designed by Iron Man, and enforced by SHIELD. And the only reason he didn't succeed was because Nick Fury was there.
"Thor the Mighty" has this:
Thor: Have you no honor?
The Wrecker: *laughs* Not even a little!
Thor: Then you should be familiar with attacking a foe from behind!
Cue Mjolnir flying back and clobbering The Wrecker upside the head.
Baldur's Colossus Climb during "The Siege of Asgard," which culminates in him stabbing a Frost Giant in the friggin' eye! The same Frost Giant later appears in the background in "A Day Like No Other," and now he's wearing an eyepatch.
The entirety of "Hulk vs. The World," such as Hulk punching off the Absorbing Man's arm, and Hawkeye descending a helicopter on a zip line.
In the "Howling Commandos" short, we get a brief clip of Percival Pinkerton owning a HYDRA mook with an umbrella.
And of course, you knew it was coming but Bucky'sHeroic Sacrifice.
The best moment is when the guys realize that they're outmatched and run outside... only to find that Hank shrunk them too without their realizing it. Later, Hank offhandedly tells Wasp to make sure they aren't eaten by his ants.
The Wasp blasting Whirlwind in the face at point blank range with one of her energy blasts in "Enter the Whirlwind".
Breakout
Now that the show has premiered, let's take a look at "Breakout". We have Thor duking it out with Graviton in full Norse God Mode, along with Wasp zapping him repeatedly to shut him up, Iron Man doing what he does best, the first time Giant Man goes big, and the Hulk showing up to turn the tide, followed by the entire team taking Graviton down.... Okay, let's face it. The entire premiere counts as a Crowning Moment of Awesome.
Special mention has to be made once more for the Hulk. The Avengers attack Graviton en masse, who simply increases the gravity around them, forcing them to the ground. As he flies up in the air, lifting a lot of debris and taunting them, Hulk starts to get back up. Graviton increases it further.. and Hulk starts to get back up. Graviton's reaction is priceless:
Captain America reawakening, then repeatedly putting Thor, Ant-Man, and Iron Man down. Sure, they weren't looking for a fight (though Thor learned faster than the others), but Cap still handed their asses to them soundly, including putting Thor down four times in less than that many minutes! And the last time he did it was a flying shield version of an Offhand Backhand!
Zemo kicking Reaper's ass.
Cap beating the crud out of Zemo after regaining his confidence.
Panther's Quest
A non serious T'Challa handles himself very well against Captain America, Iron Man, Wasp, and Giant Man. Wasp even admits he was kicking their butts.
As the battle between Black Panther and Man-Ape reaches its climax, Man-Ape pulls out a tiny sonic disruptor, which generates sound waves which could kill Panther the same way his father died. Panther falls, but lifts himself back up, and slowly walks towards his foe.
Black Panther: I am not the same man as my father, M'Baku, for my rage is greater!
After this, Panther slays Man-Ape with one more swipe of his claws.
Gamma World
Hawkeye directly threatens to take down the Hulk if he doesn't produce Bruce Banner. As foolish as that is, it actually works! Hulk laughs at him, which causes him to turn back into Banner.
Thor showing Absorbing Man why taking the properties of Mjolnir was a bad idea in "Gamma World, pt. 2".
Masters of Evil
As part of their plan to defeat the Avengers, the Enchantress poofs Hulk to Asgard to meet a couple of 50 foot tall frost giants. Later, when he gets poofed back, what happens? Does he fall out of the portal exhausted? No, he victoriously walks out of the portal covered in snow with an ice club in his hand. The Oh Crap look on Enchantress' face when he sees her is priceless.
Giant-Man kickstarting the battle by punting Abomination right through the roof and into solid rock cave wall.
Wasp taking down Crimson Dynamo by going inside his armor and blasting him point blank.
Wasp "This is gonna hurt. And I won't lie to you-I'm kinda glad!"
Zemo effortlessly taking out the Abomination with two attacks and delivering a brief Reason You Suck Speach to the brute who spent the whole episode questioning why the man with no special powers was their leader.
The Man Who Stole Tomorrow
Ant-Man summoning millions of cockroaches to defeat Kang.
Hulk throwing rocks to create an epic distraction.
Iron Man finding similarities between Kang's technology and his own, and using those connections to send everyone back to the 21st century.
Captain America has one in the beginning of episode: Kang's robots attack the entire city and they are going to destroy innocentchildren, but Captain America shows up and defeats Kang's robots. He even proceeds to say, "Avengers Assemble!" for the first time in the show.
The Kang Dynasty
Thor deflecting a beam Kang tried to shoot at the Avengers almost makes up for his constant succumbing to The Worf Effect.
The beam wouldn't have just killed the Avengers. Its power would have wiped out the entire city of New York, and according to Kang, nothing on the planet should have been able to stop the beam. Thor knocked it right back at Kang's ship. That is what having a god on your team means.
Black Panther gets a CMOA, it's just off screen. Later, when one of Kang's men is giving a status report, he tells Kang the Wakandans have forced the invaders out.
Hawkeye and Ant-Man get a joint one as Hawkeye fires an arrow at long distance through several buildings' worth of windows next to Baron Strucker- so Ant-Man can size back to normal and punch Strucker in the face.
Cap then gets one when, despite being aged ahead a few years by Strucker's artificial arm, he still owns him in one to one combat.
And finally Black Widow's line to him "By the authority of SHIELD, you're under arrest" makes her Heel Face Turn awesome.
Ultron-5
After getting trapped in a Quinjet flying into space, the Hulk busts out, and started diving right back down to Earth looking very, very angry.
Ant-Man: During the fighting in the mansion, I realized there was a flaw in Ultron's logic. Because his programming is based on the human mind, he himself is as flawed as us, and therefore part of the problem. Ultron couldn't exist in his own imperative.
Wasp: Hank, you did it! You saved the world! With science, even!
This Hostage Earth
Despite her stingers having little effect on Abomination, Wasp triggers a mini rock slide to try to fight. (It doesn't work, but still)
Hank almost literally curb-stomping the Abomination.
Zemo being Dangerously Genre Savvy enough to betray Enchantress and nearly take over Loki's operations on Earth was pretty damn cool.
Captain America showing his fearlessness and willpower when the skeletal Niffleheim ghosts arrive. Despite having the upper-hand before, Crimson Dynamo loses it and freaks out, but Cap just completely ignores the moaning spirits and beats down on Dynamo.
Cap: Always stay focused on the matter at hand, comrade.
The battle between Hulk and Executioner was pretty awesome, especially when Hulk wins by punching/tossing Skurge all the way across the lake and into the forest and taking his battle-axe as a prize.
The Fall of Asgard
Hulk with a battle-ax smashing trolls and ogres. 'Nuff said.
No, two things must be said. The trolls have Hulk pinned and one says, "The beast is strong, but not strong enough." Hulk's Response?
HULK IS STRONGEST THERE IS!!! (Cue him smashing all the enemy away)
It's an Offscreen Moment of Awesome, but Giant Man eschewing any peaceful negotiations to kick some icy cold frost giant ass in order to protect an unconscious Wasp. Also with a battle-axe.
Ant-Man: Jötunheim huh. Well guys, (grows to giant size).
Giant-Man: I'm pretty sure you're not too interested in talking this out. And frankly, (grabs the giant ice axe)neither am I!
We have a quick montage thing of the Avengers losing their individual fights. Cap has a Heroic BSOD, Tony is forced to fight without his armor etc. Except for Black Panther, who not only never recieves a solid hit from his ghost enemies, but manages to find a way out in time to bail Hawkeye and his new elf friend out by clubbing some wolves with another wolf.
To be fair, if you remember The Casket of Ancient Winters, he had no room for error, or else he would have been frozen solid, with only shows him to be just as awesome with that in mind.
Tony didn't fight too badly without his armor, at least at first. When he threatened Ulik, the rock troll laughed in his face and asked, "Who are you?" Tony answered by knocking back the beast with one blast from his remaining glove, stating simply, "I'm Iron Man."
Speaking of Tony, stabbing the arc reactor in his chest with a sword to defeat Ulik, knowing he needs that to survive was ridiculously awesome.
A Day Unlike Any Other
Captain America escaping from Nifflheim to rally the Avengers together, and using some epic teamwork to take down the giant ice wolf.
Ironman gets armor made of the same metal as Thor's hammer: Uru Armor.
Ant-Man overcoming the sonic shrieks of the ravens guarding Iggdrisil to get under the tree, grow to Giant Man, and rip it out, thus robbing Loki of his power.
The Avengers being praised as heroes by Asgard. Considering that mortals have been long dismissed by Asgardians the Avengers earning respect from the Asgardians shows how much they have accomplished.
Season 2
The Private War of Dr. Doom
Dr. Doom successfully defends himself from the entire Avengers team and the Fantastic Four. An impressive showing for Marvel's premiere super-villain.
More like everyone gets completely punked by Doom.
Earlier, when the Avengers and FF are fighting the Doom-Bots, Iron Man does some pretty cool up-close finishing moves using his replusors and jetboots.
More of an accidental CMOA, but when the heroes begin their assault on Castle Doom, Hulk and Thing are standing in the open Quinjet and Hulk pushes Thing off, sending him falling through the roof of the castle and crashing right on top of a Doom-Bot that was in the process of fighting the others.
Alone Against A.I.M.
Tony defeating Technovore, by overloading the Arc Reactor in Stark Industries. Made doubly awesome by the quote afterwards.
Rhodey: How did you know that wouldn't set off the explosives?
This episode essentially amounts to Amora and Skurge vs The Avengers and The Masters of Evil, and the scariest part is that Amora fights most of them off one by one. Scary awesome.
Executioner doesn't do too badly either, managing to hold off both the Hulk and Abomination at once. It takes a surprise attack by Zemo to finally take him down.
Ms. Marvel going up a level as The Determinator and pushing through an extremely powerful blast from Ronan the Accuser, absorbing the energy along the way.
Abigail Brand comes at a very close second, taking out the Kree invading Damocles base.
During the Avengers' battle with Ronan, Iron Man leads Ronan on a chase through the air, sharing banter, then suddenly dodges out of the way as the Hulk leaps up and slams into the Accuser, knocking him to the ground.
To Steal an Ant-Man
Luke Cage gets attacked by a thug, but simply stands with a smile on his face as the thug's punches do absolutely nothing to hurt him.
Luke: It's called unbreakable skin, fool! (cracks opponent's wrist, than hurls him into a dumpster)
The fight between the Avengers and the Guardians of the Galaxy in general, but especially the fights between Black Panther and Adam Warlock, which was essentially a stalemate, and the fight between Hulk and Rocket Raccoon, where the 3 foot raccoon was actually beating the 9 foot rage monster.
Hulk using his sonic-clap move to disintegrate Groot twice.
Hawkeye, trapped using a kitchen counter as cover, using the reflection in a dangling pot to bounce an arrow off of the ceiling and hit his target.
Who Do You Trust?
Nick Fury sneaking onboard the SHIELD Helicarrier, just to give a warning message to Maria Hill, then doing a Stealth Hi/Bye.
Ms. Marvel utterly curbstomping Griffin.
Quake also gets one for being the one to actually provoke Griffin into a rampage. Especially since she was able to punk him so easily, given that he was a pretty tough customer during the Breakout.
Cap's inspirational speech to Hawkeye, Hulk, and Wasp for keeping that part of the team together would be this, if he wasn't a Skrull.
When it looks like nobody is about to stand up for Hawkeye and it looks like he's going to get stomped to the ground, Hulk steps in and declares that he'll happily wipe the floor with anybody who tries to harm him. Doubles as a Heartwarming Moment.
The Ballad of Beta Ray Bill
The first fight between Beta Ray Bill and Thor. Then after that Bill hands most of the Asgardian elite their backsides...
... Then Odin reminds us why he's king of Asgard, disarming him and threatening that if he's harmed Thor in any way, he will end Bill there and then.