Jack Sparrow sailing majestically into Port Royal, despite his boat sinking rapidly under him, and gaining the dock with one perfectly timed step. This is widely regarded as one of the best character entrances in recent cinema.
Jack:(to the British soldiers beside him) Will you be saving her then? Soldier: I can't swim! Jack:(takes off his weapons and hands them to the soldier)Pride of the King's Navy you are. Do not lose these!
Jack escaping Norrington near the beginning.
Norrington: You are without doubt the worst pirate I've ever heard of. Jack Sparrow: But you have heard of me.
Commodore Norrington, when Jack Sparrow asks him how he can forfeit the prestige he'd get by capturing the Black Pearl. "By remembering that I serve others, Mr. Sparrow, not only myself." Yes, the strait-laced Royal Navy man beat Jack Sparrow himself in a verbal fencing match.
Barbossa standing under the falling mast, while other pirates scramble out of the way around him.
One of the film's last lines, and one that sums up Jack perfectly: "Now... bring me that horizon."
Will's attempt to set Jack free at the end. Their flawless teamwork completely makes the scene.
Governor Swann's battle with the still-animate severed skeletal hand during the climactic fight sequence.
"Gents... take a walk."
Elizabeth shows a lot of raw nerve in her response to Barbossa's instruction that she dine with him, considering that, at the time, she has no reason to think that she won't simply be chucked overboard for refusing:
Davy Jones: Let no joyful voice be heard! Let no man look up at the sky with hope! And let this day be cursed by we who ready to wake... THE KRAKEN!
Davy Jones' entrance scene.
"Do you fear death?"
Hell, just the sound of his entrance is enough to give the audience an Oh, Crap moment.
A random sailor gets a crowning moment, bravely defying Jones and gladly taking death rather than take Jones' Deal with the Devil, facing certain death with nary a hint of fear.
Davy Jones: Do you not fear death? Sailor: I'll take my chances, sir.
Will Turner finding out where the key was and stealing it from Davy Jones. Pure Guile Hero.
The entire three-way swordfight at the climax of Dead Man's Chest, not to mention the two swords, three people fight.
As awesome as the swordfight itself is, it's an even bigger Moment of Awesome for the film editor. Six different parties (Jack, Will, Norrington, Elizabeth, Ragetti/Pintel and Davy Jones's men), two different Plot Coupons (the chest and the key), as well as several other variables (the waterwheel, and often the weapons and who has them) and somehow it's still easy to tell what's going on.
Jack's return to the Black Pearl after it is attacked by the Kraken before shooting the gunpowder and rum to damage the Kraken's tentacles. See also his charge into the Kraken's maw.
Norrington, formerly the completely straight-laced navy man, manages to con Jack Sparrow - and everyone else - and make it look like an act of heroic self-sacrifice to boot, escaping with the heart while getting Jack and Davy Jones to each believe that they have it. Probably the finest act of trickery in the films, and done by the last person you'd expect.
Elizabeth gets one in this film that only becomes apparent in the next. Jack notes that everyone that came to rescue him from Davvy Jones' locker has tried to kill him at one point and they're not the only ones. Jack has a lot of enemies from the British Navy to the East India Company to other pirates and they all failed to kill him. Elizabeth is the one that succeeded.
A deleted scene expanded upon Beckett and Jack's past.
Beckett: ...I contracted you to deliver cargo on my behalf. You chose to liberate it.
Jack: People aren't cargo, mate.
At World's End
Jack's escape from Beckett's ship, if only for the one-liner immediately afterwords:
Jack: And that was without even a single drop of rum!
And the exchange before he escaped the ship:
Beckett: You're mad! Jack: Thank goodness for that, because if I wasn't, this would probably never work."
And another one for Jack after that scene, even though he wasn't there:
Beckett: Signal the Dutchman to track down Sao Feng. We follow the Pearl. How soon can we have the ship ready to pursue? Officer:(looks back towards a cracking sound, and watches as the large mast falls down; he looks on towards the Black Pearl, admirably) Do you think he plans it all out, or just makes it up as he goes along?
James Norrington gets fatally wounded while ensuring Elizabeth's escape from the Dutchman and Jones offers him a place in his crew of monsters as a chance to avoid dying. James' response? He stabs Jones — the most feared Humanoid Abomination in the seas — with his last breath as a way of saying "Screw you." Talk about an epic way to die.
Davy Jones:James Norrington, Do you fear death? ... I'll take that as a "no".
Lord Cutler Beckett's ship being blown to bits and more specifically, Beckett's death scene itself. Despite what he is, the man knows how to die in an awesome fashion. At that point in his Villainous BSOD, it was all he could do. That shot of him going down to the deck, and the final one of him before the flames engulf him, are eerie and, in a way, beautiful.
...Until you look at the panicked sailors around him and realize that a lot of them are going to die for his ego. If you must be evil, don't let's take the cream of the Royal Navy with you.
The battle at the end, where The Protagonist pirates battle against Davy Jones and his crew of undead fishmen in the middle of a thunderstorm called down by a furious sea goddess while both ships circle a whirlpool. It does not get more epic than this.
Davy Jones tauntingly calls Jack "A lost bird that never learned ta fly!" Jack responds, "Never to late too learn, eh?" and soars straight up into the Dutchman's rigging with a bit of help from a severed line. Which leads directly to Jack and Jones having a protracted sword fight on the yardarm. During said duel, Jack conclusively outfights Jones with raw skill, despite the former basically being the worst of the main cast as far as technical fighting ability goes. The dialogue right before the duel on the yardarm is noteworthy:
Davy Jones bellowing FIRE! at the top of his lungs while this magisterial piece plays. Epic indeed!
Barbossa, when he marries Will and Elizabeth during the middle of the aforementioned battle. "Just kiss!" Them marrying themselves in the battle. Also the flood of music and water when they kiss.
Additionally in this battle, as it zooms out and you get the full image of The Pearl and The Dutchmen, locked in battle, caught around a swirling vortex of doom with the afterformentioned mentioned epic music, and the sheer magnitude of the battle hits, what do you hear? Barbossa's cackle. This matches his line from earlier as they went into battle "Dying be the day worth living for!" which was pretty awesome as well.
Four more words: Pirate King Elizabeth Swann. This is Ascended FangirlUp to Eleven; she is not only a pirate but highest authority pirates the world over recognize.
The Brethren Court. Especially when Captain Teague walks in and everybody immediately shuts up out of respect mixed with fear. Even Barbossa.
An amazing Crowning Line of Awesome: "It's not just about living forever, Jackie. The trick is, living with yourself... forever."
In the final battle, there's a close up of Jack smiling and aiming a pistol at Davy Jones. That shot is a Crowning Moment without considering he manages to shoot the chest out of Jones' hand successfully.
The part where Jack guides a dying Will's hand into stabbing the heart of Davy Jones. To elaborate, the captain of the Flying Dutchman is supposed to guide the souls of those who die at sea to their resting place and is immortal so s/he can do it. The downside? Ten years at sea for one day on land. Davy Jones can only be killed by destroying his heart, and since the Flying Dutchman needs a captain, whoever kills Jones becomes the new captain.
Jack stealing the map at the end.
Jack rescuing himself and Elizabeth from the deck of the foundering Dutchman by improvising a parachute from one of the sails. Particularly ingenious since parachutes hadn't been invented yet.
Elizabeth masquerading as Calypso to Sao Feng. Not only has Barbossa, an old enemy, wagered his entire plan on Elizabeth's ability to both figure out what she needs to do and to do it convincingly, she delivers some of the sexiest, most beautiful lines worthy of any goddess. Tia Dalma would be honored.
Elizabeth has an offscreen one as captain of Sao Feng's ship. She chooses to stay with her crew in Davy Jones' brig despite Norrington's offer to use his cabin. When Norrington comes to free them, you realize that Sao Feng's crew look to her and follow her unspoken orders. In a matter of hours, in a brig on an invincible ghost ship with a crew that has betrayed her friends, Elizabeth gains their trust and loyalty. Girl didn't becomes the Pirate King for no reason.
When Elizabeth is accosted by Sao Feng's pirates before they meet with him. It looks like they're going to do something evil, then Barbossa comes in. As the pirate turns to talk to Barbossa, Elizabeth grabs him around the neck and puts a knife to his throat.
The fight between the EITC and what looks like all of Singapore, causing a city-wide battle that keeps the company busy enough for the main cast to escape unnoticed.
"Witty Jack is closer than you think". Cue Jack inverting his first MOA and standing on his ship as he sails it across land into the sea.
No love for Tia Dalma, the sea goddess herself? In her first and only real appearance as Calypso, she grows to about 100 feet, delivers what can only be assumed as the loudest and deepest "Screw You" any woman has ever uttered, turns into thousands of crabs and escapes into the sea. She then summons a maelstrom and a thunderstorm just to piss off everyone.
According to the PotC Wiki, her words are a distorted and brickwalled rendition of something along the lines of "Across the seas and storms, find the path to him that has betrayed me" (actually, the words are French, but it's mostly ominous nonsense - something about entombing evil-doers at the bottom of the water). And the rest of the scene is her taking her revenge against Davy Jones for showing the Brethren Court how to seal her in the first place.
Blackbeard declares that "Mutineers hang!", and the entire ship turns on and grabs the mutineers with living ropes.
That entire scene is a crowning moment for Blackbeard. Jack's mutiny seems on the verge of success, Jack declares 'the ship is ours!', and then the doors behind him open. All we see is a silhouette, and that silhouette slowly walks forward to reveal Blackbeard, casually sipping rum while embers burn in his beard:
Blackbeard: Gentlemen. I be placed in a bewilderment. There I were, resting, and upon a sudden, I hear an ungodly row on deck. Sailors abandoning their posts, without absence, without leave (clutches his sword's hilt, causing the ship's ropes to coil and twist). Men before the mast, taking the ship for themselves. What be that, First Mate?
First Mate: Mutiny, captain!
First Mate: Mutiny!
Blackbeard: Ah. Mutiny, is it? And we all know what fate befalls mutineers. Mutineers... hang!
One mutineer even tries to jump overboard. The ropes lash out, snag him, and hauls him back in.
Jack deserves one for his completely calm snark while hanging upside down. The man's fought krakens, come back from the dead, been worshipped as a god and almost eaten, and become an immortal zombie. A ship coming alive? Nothing new for Jack Sparrow.
Jack: Captain, I wish to report a mutiny.
The moment "Mr Smith" enters the courtroom and we guess who it is. And much of the following 20 minutes.
Jack's escape from the palace as "He's a Pirate" plays.
Heck, the whole chase scene, culminating in Captain Teague stepping in to save his son from a lingering sniper.
Jack's duel with an imposter of himself (Angelica in disguise) is a deft display of swordplay that reminds us that Jack can rely on more than his wits.
One of Gibbs' best moments is when, before his intended hanging, he burns the map before the others can do anything, and he tells Barbossa, "I've had just enough time to memorize it. Every route is saved safely right here." (Taps his head.)
The swiping of the silver chalices, complete with a very nice Bash Brothers moment between Jack and Barbossa.
"Someone make a note of that man's bravery." Because you know what? It took guts to jump in front of about a hundred Spanish soldiers and claim the Fountain for England. This is the same officer who stood by Norrington as Jack stole a ship at the beginning of the Curse of the Black Pearl and commented on him being the best pirate he's ever seen. He was the same guy who stood by Beckett as Jack escaped on the Pearl AND crippled Beckett's Man-o-War and wondered if he plans it all out or just makes it up as he goes along. After three films of just admiring Jack's badassery, he finally gets a awesome moment of his own!
The Spaniard's unwillingness to be corrupted by the promise of living forever with the use of the evil artifact. He nonchalantly topples it like he does this every day.
Phillip dressing down Blackbeard, just moments after he was strung to the mast for who knows how long. He leaves Blackbeard speechless. Later, he steals a sword from one of Blackbeard's crew just to get Syrena some air, then wedges in his Bible with perfect timing when the pirate takes his sword back.
The entirety of Blackbeard's and Barbossa's fight. For a brief moment you think, "Barbossa is a cripple, he's screwed", then Io and behold, there you see Barbossa Dual Wielding his crutch and his sword against Blackbeard with enough mastery to make any other character jealous. There are to specific moments that illustrate this: