Bilbo, alone and armed with an Elvish dagger and a magic ring, versus a cluster of giant spiders in the darkest part of Mirkwood Forest ... and the spiders never stood a chance! They even become terrified of the newly christened Sting! (Plays out similarly in the animated movie.)
Bilbo managing to evade the notice of the Mirkwood elves for weeks while successfully finding a way for him and his companions to escape.
Bilbo walks alone into a dragon's lair. A dragon, mind you, that managed to destroy two great kingdoms and their armies in a single day. Alone and with only a magic ring, Bilbo goes into Smaug's lair not just once, but twice and manages to hold his own in speaking with the beast who turns out to be cunning as well as powerful!
The Battle of the Five Armies, with the Humans, the Elves, and the Dwarves in a hastily forged alliance against the Orcs and the Wargs. And just when everything seems lost, Bilbo sees something on the horizon. What he says next serves as a very short Rousing Speech and a Battle Cry for the gathered forces.
First he raises the alarm when he realises that Smaug is coming, so that Laketown has time to prepare itself, then keeps encouraging the soldiers and archers not to lose hope as they try to bring Smaug down.
And then, when everyone else is fleeing, he's still firing arrow after arrow as the flames draw nearer, refusing to give up. When he learns the secret about Smaug's weakness he makes the shot that finally kills Smaug, fully aware that he'll probably die as well when the dragon collapses on the town; he was ready and willing to give his own life to save his people. Originally he was meant to die, but Tolkien himself recognised how awesome Bard is and kept him alive for the finale.
Smaug's assault on Erebor and Dale is every bit as glorious as it is horrifying. He singlehandedly razed not one, but TWO of the most powerful kingdoms in Middle Earth within an afternoon. Sauron himself needed a huge army and years of planning to attempt to overthrow Gondor... but who needs countless minions and intricate plans when you are Smaug the Magnificent?
If you know his backstory, it becomes a very dark sort of awesome. He was one of Morgoth's Fire Drakes, creatures who fought alongside Balrogs as shock troops for Sauron's boss - "I laid low the warriors of old..." Destroying whole kingdoms was his job, and he was happy to keep doing it long after Morgoth had left the picture.
Furthermore, it's implied that he only assaulted Erebor because King Thrór amassed an obscene amount of wealth; the only reason he didn't do so sooner was because he didn't deign it to be worth his time. He literally destroyed the greatest dwarven nation in the world on a whim.
Smaug: I kill where I wish and none dare resist. I laid low the warriors of old and their like is not in the world today. Then I was but young and tender. Now I am old and strong, strong, strong!
And even before that, when Bilbo shows some Guile Hero qualities and tries to put the trolls off eating the dwarves by insisting they have parasites. Of course, that nearly gets him eaten instead, but it was still pretty quick thinking.
Really, seeing the dwarves furiously charge out of the undergrowth to rescue Bilbo (which culminates in an epic fight), when compared to the original book where they all got caught with relative ease.
Dori gets a good shot at one of the troll's unmentionables with his bolas. And then Dwalin knocks its teeth out with his war-hammer.
The dwarves preferred method of freeing comrades who were grabbed by trolls? Launching themselves bodily into the air, and then slicing the troll's arms so they'll drop'em.
It's not in the final film but video blogs show Glóin throwing his biggest axe to Fíli, who jumps onto Kíli's shoulders and proceeds to calmly smack one of the trolls in the face with it. Hopefully that one will make it to the EE.
Three trolls were all it took in Return of The King to scatter the Gondorian knights guarding the gates of Minas Tirith (though those were the New and Improved breed, immune to sunlight, trained and armored for battle). This Ragtag Band of Misfits would have made the fight a Curb-Stomp Battle if Bilbo hadn't gotten caught.
"Far over the misty mountains cold...". That whole scene has the power to make even the rowdiest cinema audience go completely silent and listen to the haunting beauty filling their ears.
The "Blunt the Knives" song. It's the scene where the dwarves reveal that they can match Legolas from LOTR in terms of dexterity, tossing around plates and fragile china one dwarf to another (Balin not even paying much attention as he does so) and it all ends up in a neat set of piles at the end.
Radagast vs. the Witch-King of Angmar. A hippie wizard gets ambushed by the spirit of pure evil, takes him down with a few blows from his staff and escapes.
And let's not forget the chase between the wargs and his rabbits. He manages to outrun the wargs.
The entire escape from the goblin caves is filled with Crowning Moments every five seconds: they were quite literally being swarmed at every conceivable angle and opportunity, yet none of them suffered anything more than a few scratches - they weren't even out of breath!
Gandalf. This is the first time he uses Glamdring, and how well does he wield it? He slices through a goblin. The goblin panics silently, trying to process both the fact that he knows a sword went through him, and that he doesn't have a mark on him. Gandalf gently taps the confused goblin on the head, and the head tumbles off, neatly severed at the neck.
Gandalf blasting a large boulder out of the walls, and giving the orcs first-hand experience in the life of Indiana Jones.
Kíli BLOCKING ARROWS WITH HIS SWORD! And then with a LADDER! And then using the ladder to push goblins off a chasm! And then using the ladder to cross the chasm!
Bombur running along, and when he's dogpiled by a swarm of smaller goblins, he just keeps running!
Balin, the oldest dwarf in company, who wears no armor but a simple red robe more suited for a wizard then a warrior, flourishes his scimitar and with one hand takes out the five or six goblins that were surrounding him.
Dwalin when encountering a particularly large group of goblins sheathes his axe and picks up a big plank of wood and starts swatting the goblins off the edge as he charges into them.
Óin, one of the eldest and most infirm of the Company, takes out a whole crowd of goblins just by swinging his staff around his head and building up a bit of momentum.
Speaking of those scenes, seeing the special effects with the Great Goblin and the trolls talking were amazing. In the earlier films, there seemed no possible way that they could sound like normal people, only like trolls and orcs. Seeing them talk like regular humans made them really scary and cool at the same time.
Thorin charging Azog across a burning tree after Azog taunts Thorin that he encountered Thráin (Thorin's father), and that Thráin "stank of fear".
From that same scene, Bilbo flinging himself at Azog's lieutenant in an attempt to save Thorin's life - and it WORKS! Plus when he defended himself, he stabbed the orc not once but three times.
And his example inspires most of the other dwarves to follow him into battle, instead of simply hanging for their lives.
Every scene with Azog, period. Not only is he quite the Adaptational Badass from a token mention in the book, but (related to the above point on special effects) he looks very real for a being that's purely computer-generated.
Related: Thorin showing us how he got the title 'Oakenshield'.
The entire scene where the eagles rescue the company. Shows you exactly why the great eagles are such powerful allies, and why Tolkien referred to them as a "dangerous device" for his narrative.
The fact that they were shown to be intelligent, one using the power of its wings to roast several wargs in an inferno, and another physically uprooting a tree to squash several of them instead of just attacking a single orc. It's awesome for those of us who haven't read the books and didn't know the eagles were an actual race instead of a summon spell.
The cinematography for the eagle scenes alone are a gorgeous sort of awesome.
One for the elves when they ride out to eliminate the orc scouting party chasing the dwarves. They completely slaughter the orcs with almost no effort.
Gandalf outsmarting Saruman by predicting he'd try to stop the dwarves from reclaiming Erebor and sending the dwarves away from Rivendell ahead of time. Not even Elrond and Galadriel caught onto his plan until it was too late.
The cameo of the Necromancer is as awesome as it is creepy. He barely appears, all we see of him is shadow and yet he manages to steal the scene.
Bilbo sparing Gollum's life. It doesn't seem like much on its own, but then you remember this is the action that would eventually save all of Middle Earth.
The flashback to the Battle of Azanulbizar is full of this. Most notably Thorin using an oak branch as a shield and taking off Azog's arm.
On top of that after Thrór's death, the dwarf army begins to rout, but once he cuts off Azog's arm, Thorin stands up and rallies his army, shouting a Dwarvish Battle Cry and leading them to victory.
Dwalin can be seen in the background of several shots headbutting any orc that gets in his way.
For the orcs, Azog is seen knocking two dwarves into the air with one swing.
A meta-example is how much more of the original lines from the book got into the film compared to The Lord of the Rings trilogy. Bilbo starting his book with "In a hole in the ground there lived a hobbit", closely followed by Bilbo and Gandalf's argument over "Good morning", were a gratifying Establishing Character Moment for the film itself for long-term fans.
Bilbo's short speech to the company manages to perfectly encapsulate the philosophy a hobbithero would have. It's not a big declaration or a promise to eradicate some evil or enemy, there are just people who don't even have the simple comforts of home and he would like to fix that.
Bilbo Baggins: ...I often think of Bag End. I miss my books. And my armchair. My garden. See, that's where I belong. That's home. And that's why I came back, 'cause... You don't have one. A home. It was taken from you. But I will help you take it back if I can.
Smaug knowing exactly where Bilbo is despite the Ring thanks to his Super Senses. And Smaug knowing exactly what's happening with Sauron half a country away, and even knowing what the One Ring is and even capable of identifying who sent Bilbo and what he is after! Yes there is a reason why Gandalf wants him to be killed! If Sauron gets Smaug on his side, the world is doom.
The Mexican stand-off between Smaug and Bilbo. Surrounded by mountains of gold, a scared Hobbit on one side, and one of the most dangerous dragons in the history of the world on the other. The Arkenstone between them. Bilbo is awesome simply for standing his ground at that point, while Smaug coolly ponders whether or not to just give Bilbo the Arkenstone and kill Thorin later. Then Smaug brings out his fire, and Bilbo brings out his Ring.
The winner? Bilbo, who stole the Arkenstone and slipped away invisibly.
Gandalf single-handily infiltrates Dol Guldur, and boldly commands the evil within to reveal itself. What happens when it finally does? We get to see Gandalf taking on Sauron himself in a magic duel. And while he is defeated, Gandalf does manages to hold off Sauron for a surprising length of time.
Likewise, everything regarding Sauron. He initially appears as a mass of evil, tendril-like smoke, and then appears in his armor-form, while also on firethat forms his Lidless Eye. Much like his first appearance, he completely stole the show.
The dwarves infiltrating Erebor, and then taking on Smaug by burying him under a tidal wave of liquid gold. Sure, it didn't work, but at least they tried.
Thorin FINALLY being able to face Smaug, a hundred and seventy years after he took Erebor.
Thorin: I am taking back what you stole!
Legolas is just as badass as he was in the other movies. Among his other accomplishments, he manages to headshot two orcs with the same arrow, the tip skewering the first and embedding itself in the one behind it.
At another point, he kills one of the orcs that attacked Bard's house and sends him flying over a ledge to land on a boat below, causing another orc on the boat to be sent flying into the air. Legolas then decapitates this orc by swinging a couple of daggers at just the right moment.
Bard displays great accurancy with his bow, appearing like Legolas' long lost human brother.
He's Bard the motherfucking Bowman! More like Legolas is HIS long lost elvish brother.
Bard practically runs Laketown. He has the Master's eye on him, with spies everywhere. Yet he still manages to sneak thirteen dwarves and a hobbit into town, all while jauntily waving at the spies trailing him.
The Master of Laketown is concerned that Bard could lead an uprising. Given the way he gets away with bringing a boatload of illegal fish into town, as well as the fairly impressive weapons cache he hides in the same spot the spies looking for him fish, he's not wrong.
Bard turning around a threat from the Master's lacky, pointing out that sure, the Master knows where he lives, but it's a small town, and he knows where the Master lives as well.
Bard figuring out who Thorin is, and trying to stop him from going to the mountain. And then when that fails, helping Thorin's sick nephew despite the trouble he's about to cause.
Bard in general.
Bolg actually coming close to killing Legolas, who up until this point in the series seemed pretty darn indestructible.
After failing to kill the elf, he neatly breaks away from the fight and simply strolls away like a boss.
More than that but when Legolas stab him in the gut, which has shown to pretty much insta-kill every orc so far, Bolg just literally knocks him back and lets the other orcs handle him as his main goal(Thorin) wasn't there. He also made Legolas BLEED! You can see Legolas stare in shock at his own blood. There is a reason why Azog chose him to handle Thorin.
Kíli soldiering on with his arrow wound.
Beorn being so terrifying that a whole band of orcs that were perfectly willing to attack an elven stronghold are afraid to attack him.
And Gandalf stopping a pair of assassin bounty hunters from killing Thorin just by being in the same room.
Bilbo saving the dwarves from the spiders, then the elves, and then figuring out the riddle / Prophecy Twist to find the entrance to the mountain. They would have been screwed several times over, if not for him.
Bombur kicking ass during the barrel chase sequence.
That entire sequence in general, really.
Considering the early concerns whether a canon foreigner would be able to "keep pace" with the classic book characters, all of Tauriel action scenes are awesomely performed by Evangeline Lilly. She fires arrows while running, parkouring and sliding at lightening pace and is terrifying in close quarters with her knives.
We get a flashback where Girion, the last King of Dale, repeatedly tried to bring Smaug down by firing ballasts even as the dragon destroyed his city, refusing to give up and fighting until the moment he died. Thorin and the Master of Laketown consider this an abject failure considering he failed to kill Smaug, but he probably came closer than anyone ever has to actually doing it. And furthermore, he made it that much easier for his descendant, Bard, to finally succeed.
More than that, since if you watch that scene closely, you realize that Girion actually managed to HIT Smaug successfully with every arrow, it's just that Smaug's scales were so damned tough that it only managed to remove them. But later, when Bilbo sees the chip in his scales and remarks that the legend of the black arrows are true, Smaug flips his lid. Girion may have failed, but when you manage to not only hurt a dragon the size of a city block, whose power and evilness is second only to Sauron, and to actually make him freak out when the word "black arrow" is spoken. You are BADASS!