Issue 4 of The Avengers has the iconic image of Captain America being frozen in ice, as the Wasp recognizes him. When he wakes up, he assumes the worst and attacks the Avengers, catching them massively off-guard and basically beating everyone there up. He was only stopped by the Wasp growing to her full size in front of him, causing him to hold back and come to his senses.
What If? #44, "What If Captain America Were Revived Today?". Cap is not revived out of suspended animation until the mid-80s, and discovers that the country has been willingly turned into a police state, led by a paranoid, substitute Captain America who's being manipulated by an organization out to stifle dissent, curtail civil rights, and protect the privileged. Identity cards are issued, martial law is declared, minorities are placed in walled ghettos, and anyone siding with them (including other superheroes) are either imprisoned or hunted traitors. Upon learning of all this, the real Cap leads an assault during a nationally-televised rally, whereupon he defeats the impostor and then chews out the entire country for betraying its ideals... then rallies the country back to those ideals. And he makes it work.
Well, I say America is nothing! Without its ideals — its commitment to the freedom of all men, America is a piece of trash! A nation is nothing! A flag is a piece of cloth! I fought Adolf Hitler not because America was great, but because it was fragile! I knew that liberty could be snuffed out here as in Nazi Germany! As a people, we were no different then them! When I returned, I saw that you nearly did turn American into nothing! And the only reason you're not less than nothing — — is that it's still possible for you too bring freedom back to America!
And after that speech, when the crowd is cheering Cap on as their new leader, he turns them down — because blind acceptance of leadership was what got them into the mess in the first place.
And then, Cap and Spidey team up with an army of rebels to kick racist ass.
The very first Cosmic Cube story had Captain America fight the Red Skull, who'd been made all-powerful thanks to the Cube. Nothing he tried worked, so eventually he surrendered... and used the window of opportunity from kneeling to knock the Cube out of the Skull's hands.
Trust Captain America to find nobility in his own assassination. Cap, restrained and walking up the steps of a courthouse to face trial for rebelling against the Superhero Registration Act, sees a laser sight targeting one of his guards. Not hesitating for a moment, Cap throws himself into the path of the bullet, making his last act saving an innocent life at cost to himself after having already lost so much.
How about Rebirth, when he finally regains control of his own body, leads the charge against the Red Skull and the public sees him and notes, "Can it be? It is! It's Captain America!".
And let's not forget the battle against the Giant Red Skull itself, as Cap leads his allies in defeating the Skull, as only he can.
Before that, we get a glorious full-page spread of both Steve and Bucky, both of whom are in their Captain America outfits, and both ready to kick the Skull's ass.
Doesn't matter what the press says. Doesn't matter what the politicians or the mobs say. Doesn't matter if the whole country decides that something wrong is something right. This nation was founded on one principle above all else: the requirement that we stand up for what we believe, no matter the odds or the consequences. When the mob and the press and the whole world tell you to move, your job is to plant yourself like a tree beside the river of truth, and tell the whole world - "No, you move."
Captain America #251-252 had Batroc the Leaper working with Mr. Hyde, who threatened to ram an oil tanker into New York City and blow it up. Their only demand was that Captain America surrender himself, and when he did they chained him to the front of the ship. Hyde then planned to ram the ship into the city anyway, and when Cap broke free, Batroc revealed that he knew Hyde would double-cross him, he couldn't stand to see him murder so many innocents, and he specifically requested Captain America's presence because of all the heroes out there he knew he'd have the best chance at stopping Hyde.
Another Crowning Moment for Cap was during The Infinity Gauntlet saga. Thanos, the now-omnipotent servant of Death, has slain all of Marvel's surviving heroes. Only Captain America remains, and he knows he has no chance of winning or surviving. Still, he strides forward and stares Thanos in the eyes.
Cap: As long as one man stands against you, you'll never claim victory.
Thanos: Noble sentiments from one who is about to die.
Cap: I've lived my life by those words. They're well worth dying for.
James as Captain America saving both Barack Obama and John McCain from the Red Skull's assassins, declaring, in response to the question "Who the hell are you?": "I'm Captain America!"
Later, he heroically leaps in front of a rocket aimed at a limo carrying said presidential candidates, and saves them, ultimately winning the approval of bystanders and government agents, who praise Cap for a job well done.
On the cover of his very first issue, he is punching out Adolf Hitler. 'nuff said.
For full context, this was in 1940, before America entered World War II.
In context, Steve knocks down a FIFTY FOOT TALL Hank, who thought that transforming into a giant would stop him from being beaten senseless, and does just that to the brute.
While aboard a SHIELD helicarrier, Cap is asked if he will help round up his friends who violate a law that is yet to pass. Cap is reluctant and repeatedly tries to defuse the situation, but the commander on deck just wants to hear him say yes. Cue five pages of Cap demonstrating why he's not called Technician Fifth Grade America, followed by leaping out a window and landing on a fighter jet that is about to land in the carrier's hanger, putting his shield through the canopy to hold on, chastising the pilot for taking the Lord's name in vain, and commanding him to keep flying. He later had the pilot land the jet safely in a football field and took him for some burgers and fries. And if that doesn't make you wish Cap was your dad, nothing ever will.
In New Avengers Vol.1, Spiderman's been thrown into the midst of a ton of villains. Suffice it to say, he's getting his butt kicked. And then the shield blurs into frame and we get treated to practically a full-page spread of Cap making his entrance, S.H.I.E.L.D agents right behind him.
Captain America: This ends NOW!
Cap, recently back from the dead, leading the Avengers new and young to aid Asgard and making his presence known by hurling his shield against Norman Osborn, who in the meantime has taken up the identity of the Iron Patriot (a red, white and blue Iron Man armor), shown in slow motion as the shield is reflected in Osborn's faceplate.
Framed for treason, Cap has his American citizenship revoked and exiled out of the U.S. After a bout of self-pity, he goes on the attack to find out Machinesmith is behind this. The robot then attacks Camp David, taking out the Secret Service and downing a helicopter and then steals the "nuclear football" with the codes taken from the President's head (which proves Cap's innocence). Machinesmith gloats that he can set off WWIII and let the machines rule. His rant is cut off when he sees a shield-bearing figure slowly march through the flames of the helicopter...
Cap's Crowning Moment of Crowning Moments came when he, fighting alongside Thor against trolls or something, was able to throw Mjölnir toward Thor, Mjölnir being a mystical hammer that can only be lifted by those deemed worthy by Odin. That's right, Rogers was deemed worthy and honorable warrior by a god king, while Odin's son Thor, for a long time, was not.
In the Super-Soldier mini at the start of the Heroic Age, Steve has his Super-Soldier serum deactivated, turning him into the same skinny unimpressive kid he was in the forties before the war. He is mocked and manhandled by guards four times as big as he, themselves on Super-Soldier serum, and as they are shoving him to his death, he muses that it was growing up in the harsh environment of depression era Brooklyn that made him the man he is, and that the Super-Soldier serum gave his strength and speed, but his fighting prowess came from months of training. And then he demonstrates.
From the climax of the first story-arc in Secret Avengers, we have Steve (at the time, serving as the man in charge of America's superheroes) temporarily gaining the powers of the Nova Force in order to save his team from a Serpent Crown-possessed Nova. It's as crazy flippin' awesome as you can imagine.
In the JLA/Avengers crossover, he has two... first, he earned the respect of the Goddamned Batman, enough to investigate the problems afflicting their universes. And two, the unified JLA and Avengers need someone to coordinate their battle efforts. Instead of Batman or Superman, who will be on the battlefield, they choose Cap. When a force that has both Superman and Batman are willing to let someone else coordinate their war for reality, that guy is probably awesome beyond awesome.
While taking down Prometheus (who once crippled the JLA using his Martial Arts As Programs tech):
From his very first fight with Baron Zemo (back when he was still Doctor Zemo):
"I fought your kind, Zemo! I fought you every day of that war! You said Americans were weak! You said we could never fight for freedom. Well, feel this grip tyrant! It's the hands of a man who loves his liberty! Look into my eyes, and know that I would die for my freedoms! The world must never mistake compassion for weakness! And while I live - it won't!"
His cameo in Skrull Kill Krew. He's introduced quietly eating a big dish of home-made apple pie at an airport diner. Cue mocking cynic's appearance - "how DARE you wear the flag of such an evil, fascist nation", yadda yadda yadda. Cap, quietly: "I don't stand for the flag. I stand for the DREAM." Cue massed attack of HYDRA minions on airport. Cue Cap wiping the floor with those minions in the diner before finishing his pie, paying, politely saying goodbye and charging out to deal with the rest of them. Cut to previously mocking young waitress, eyes wide: "...I want to have his children." Just brilliant.
Here's another one for Bucky as Cap. In New Avengers #58, as the team is trapped with the Dark Avengers in a sewer, Ares tosses his axe straight for them. Bucky manages to block it but is knocked over from the sheer impact. As Ares calmly strolls over to finish the job, Bucky, who was Playing Possum, sticks his gun under Ares' chin and empties the magazine into Ares. Ares keels over, face-first into the sewage, and manages to blurt out an embarrassed "Impressive." as Bucky and the team escape.
As for Captain America as a One-Man Army, look no further than in Tales of Suspense #62 when he is in a high security prison where the prisoner of Cell Block Ten have seized control, thrown Cap in a cell and taken his shield, convinced that it could get the main gate open. Just when they are wondering why it's not working, Cap sudden appears, bounding on the heads of the cons saying "Would anyone care to ask me?" In that area, Cap is outnumbered dozens to one with automatic weapons; they didn't have a chance.
Cap's so awesome, he gets these while he's dead. During World War Hulk, several people were discussing strategies for taking out the Hulk, who was so angry that he was able to strength his way through anything. It was mentioned that if Captain America was still alive, he would be able to stop the Hulk...simply by standing in his way. Captain America commands so much respect that he would be able to stop the Hulk at his absolute angriest just by being there.
Another moment of awesome for Cap during the same arc. When Rick Jones arrives to try and talk Hulk down, one of Hulk's companions gives Rick a "The Reason You Suck" Speech, and ends it off with ""Who sent you? Captain America?"" to which Rick responds, without even looking at the other guy, straight into Hulk's face ""Captain America is dead"". At that moment, Hulk's face, livid with barely bottled up-rage, softened up with genuine grief. Even for a second, it shows much respect Cap commands from everyone
Not an isolated incident. Back when he went missing in the ice and everyone thought he was dead, another guy took his costume and pretended to be Cap for the public. Despite believing that he couldn't keep up. A villain uses future tech to almost trick the replacement, offering him the chance to give his life to bring back Cap. Luckily the villain gets found out in time, but still.
In the finale of Fear Itself, despite Earth's almost inevitable destruction by the hands of either the Serpent or Odin, Captain America travels alone to Broxton to help the civilian militia defend their town. When the Serpent's forces approach, Cap tells the militia that he won't fault them for fleeing to be with their families, but kindly asks them to at least leave their weapons behind. All of them leave except for one man, who stands by Cap because he realizes if he leaves now, he'd never be able to live with his cowardice. During the actual battle, Cap leads the other Avengers, and because his shield was destroyed earlier, he picks up Mjölnir as his replacement weapon. Meanwhile, the people of Broxton are watching the battle, and ashamed of their cowardice, actually charge out of their homes and fight side by side with Cap and the Avengers against the Serpent's forces.
Cap's epic verbal beatdown of Odin was equal amounts of CMOA and CMOF. And then Odin did exactly what Cap said. When Cap commands, even gods of gods listen
While this one doesn't feature Captain America, it did take place in his title. During the Acts of Vengeance crossover, amongst the villains working together were Magneto, a Holocaust survivor, and the Red Skull, the cruelest Nazi in the Marvel Universe. Magneto uses this opportunity to beat the living crap out of Red Skull and imprison him in an oubliette with only the barest amount of supplies so that he can think about his crimes before he dies down there.
At Cap's funeral is a Holocaust survivor whose memories go back to 1945. We see a double page splash panel as Captain America is leading the attack on her death camp, leaping against the enemy, grimly determined to finally stop the horror before him.
The climax to an arc where an opportunistic Skrull decides to impersonate Cap and use his name to cause chaos in the United States naturally has Cap exposing said Skrull and beating him, with the help of the Avengers and The Thing. This is followed by a speech where he takes full responsibility for letting the new-found fame (which had turned him to a superpowered celebrity) get to his head, allowing the Skrull to use that to his advantage. Cap ends the speech (and subsequently, the issue) by outlining that he's not a superhero, but rather a man of the American people, ready to help make the American Dream and turn it into an American Reality.
"So let's get this straight: Captain America, apparently deciding that Punching Hitler wasn't giving him enough of a challenge, decided to take ANOTHER level in badass, go straight down to hell, and beat upSATAN HIMSELF."
During the "Red Zone" story arc, the Secretary of Defense, Dell Rusk, has revealed himself to be (big surprise), the Red Skull, spreading a virus as part of his plan to turn the U.S. into his own twisted country. He stands outside a window, admiring the Washington Monument, a hand to his heart as he talks of how this will be "my America." Cue the window shattering inward and one-pissed off Cap: "Skull. Don't you DARE salute that flag!"
Captain America was on an amphibious lander with the Howling Commandos. Picture the scene: before dawn, first Tuesday in June, 1944. Some no-name boat. Then, just before dawn, this happens:
"I am not afraid to die this day because what we do here is necessary. Look at me. I'm just a man, but I believe that one man - one man with enough conviction - that one man can win a war. Give that man a group of soldiers with the same conviction, and you can change the world. You fellas know where I can find some soldiers like that?"
One from outside his own title that, while represented on the arc's own page, bears repeating: During the Born Again arc of Comic Book/Daredevil the Kingpin through some of his contacts unleashes the Ax-Crazy, flag wearing super soldier Nuke. After deeating the man and watch his heart give out due to the pills that powered him, Cap storms a military base and confronts the general responsible, leading to this iconic exchange.
General: You know the department holds you in the highest regard. We've always valued your commitment — and your loyalty...
Captain America: I'm loyal to nothing, General... except the dream.
The flashbacks to Steve's mom, Sarah, in the Dimension Z story line. They are, on the whole, horrible: Steve's dad smacks his mother around because she's railing at him for not finding work. He throws off excuse after excuse about people not wanting to hire Irish and how her wages aren't enough to support the family, either, and she calls him on that, too. She calls him on the fact that he doesn't ever get to work on time when he has a job because of his drinking, and he keeps knocking her to the ground until her face is bloody. But she keeps getting up and refuses to back down, because, dammit, she's right. She's getting beat up, but she isn't a beaten wife. She stands up for a final time, tells him straight-up that he better try going to work sober, and Joseph Rogers turns around and leaves. Afterward, she cuddles Steve and when he asks why she doesn't just stay down so he'll stop, she tells him: "You always stand up." In a later flashback, she tells Steve that Joseph allowed bad circumstances to change him from a good man into a weak one. So not only was Sarah Rogers brave enough to stand up to her husband and determined enough to shame him for hitting her, but she was also big enough to forgive him, knowing that he wasn't as strong as she is. In a genre where Uncle Ben and Jor-El tend to get all the credit, it's pretty amazing this comic tells us in no uncertain terms that everything heroic about Steve, everything that makes him Captain America, he learned from his mommy.
One for the new Captain America, Sam Wilson - Sin, the Red Skull's daughter, attempts to ruin Sam with the whole "Snap Wilson" bit, but he comes back in style, taking her down.
Sin: But, you've always wondered, haven't you? In quiet moments. "Is it true?" "Is that me?"
A metatextual moment of awesome for writer Rick Remender here, who revealed in an interview that he read the "Snap Wilson" story as a kid and was offended by it even then, and that when he became a writer he was constantly looking for any excuse he could find to retcon it out of existence. When he got that chance, he naturally leapt on it without hesitation.
In one issue, he gets a hold of the newest issue of the Daily Bugle, and is very much not pleased with what's on the front page...
Captain America: Mr. Jameson. I'd like to talk to you about this headline. (slaps paper down on the desk in front of him) Jameson: What, uh, what about— Captain America: I was with Spider-Man yesterday. We took down M.O.D.O.K. and an A.I.M. cell...together. He's not a menace. I know what a menace looks like. So...why don't you grab a pencil... (The next day, Spider-Man is relaxing in a web hammock reading the new Daily Bugle, with the headline Captain America and Spider-Man save city from M.O.D.O.K. — "Spider-Man is an asset to New York.") Spider-Man: (flashes A-OK sign at Jameson)