"Pilot": Oliver taking down his first target's guards while storming his penthouse, ducking in and out of their gunfire like the wind, then finally taking on Constantine Drakon and killing him with an arrow to the chest.
"Honor Thy Father": Diggle taking down two Triad assassins and then mixing it up with China White. She outclasses him, but he still held his own for a while.
Seeing Laurel kicking ass was a refreshing change, with hopes high for seeing her take on her own superheroine mantle.
Arrow versus Deadshot: Ollie sends an arrow right through Deadshot's eye. And out-draws a wrist-mounted machine gun beforehand!
Or not...Deadshot was aiming for DIGGLE with his last volley!
Likewise, their rematch in "Year's End" though he loses this time. Though not quite the same one-on-one fight since Wintergreen had a few henchmen with him.
Arrow vs Dark Archer in "Year's End".
Diggle playing Oliver to get him invested in the Royal Flush Gang case: He arranges for the police officer who was injured in the last robbery to be transferred to a better hospital, paid for by Oliver, and then he tells Oliver a lie about his next target attempting suicide to get him to come to the hospital, where he meets the officer's wife. When Oliver calls him on it, Dig reminds him that he's working with Oliver, not for him, and what kind of man Diggle is. An excellent reminder that Diggle is more than just Oliver's bodyguard, he's his conscience.
"Burned": Oliver He's Back moment, getting over the PTSD he's been suffering from ever since his fight with Dark Archer and stopping Firefly from killing his final target. Especially notable is that at the beginning of the episode, it's established he's lost his Improbable Aiming Skills, but he makes his entrance here by shooting Firefly's lighter out of the air as it's thrown at the fire chief, knocking it clear away.
The scene before that makes it better. Diggle tries to stop him from going by proving that the drugs will screw with his aim, and challenges him to hit a tennis ball he holds up near his face. Ollie aims, realizes he can't aim at all, and puts the bow away. Diggle is relieved, then Oliver just says, "You should remember one thing: I don't need the bow." Then he suits up and leaves an exasperated Diggle behind. That's right, he took down Vertigo WITHOUT HIS TRADEMARK ARROWS. That's how awesome he is.
"Betrayal": The raid on Cyrus Vanch's mansion:
Vanch: "He's going up against trained men with their fingers on the trigger of guns that fire up to 600 rounds per minute. Now I'm no Einstein, but that is a lot of bullets."
*Gilligan Cut to Ollie taking out the first round of guards*
Vanch: "And even if he were to take them out, I have two sharpshooters on the roof."
*Ollie takes out the snipers*
Vanch: "But even if he were to get by them, what's he gonna do against the veritable army of sons of bitches I've got waiting for him?"
Vanch: "Now, as I said, I'm no Einstein, but I can count to 24. And in case you're wondering, I was, so I studied up on my news footage. 24 is the exact number of arrows he carries in his quiver and flechettes around his forearm."
The Hood: "MOIRA QUEEN! YOU HAVE FAILED THIS CITY!"
What could be Island!Ollie's first real Moment of Awesome (well, second if you count him not betraying Yao Fei in spite of being tortured by freakin' Wintergreen): At this time, he has no fighting technique yet, is tied to a chair, and has just been beaten by Slade Wilson, who is about to kill him so that Oliver won't betray him. Ollie dislocates his shoulder to free himself and punches Slade, who isn't affected at all, since Ollie doesn't know how to fight yet. It allows Ollie to earn Slade's respect and teachings.
"The Odyssey" is just one long episode of awesome:
When Oliver stands on a land mine and is cornered by some of Fyers' Mooks, Slade seemingly abandons him... only to come back and take the soldiers by surprise, killing them and tossing one on top of the mine so it doesn't explode when Ollie gets off.
We continue to see Oliver go from spoiled playboy in over his head to the beginnings of a true hero — Slade is planning on calling in an airstrike on the island once they get on the resupply plane to escape. However, Oliver refuses to leave without Yao Fei, and gives a speech about why. And then later, giving a brief "The Reason You Suck" Speech to Wintergreen/Deathstroke.
In the flashback, Oliver's plan to use the missile launcher's circuit board as leverage.
Team Green Arrow deduces that the killer of the week is using the subway network. Felicity, in particular, is happy to have redeemed herself (in her eyes, even if Ollie doesn't think she could have done any better than she did, crackerjack IT genius that she is).
Oliver breaking down every office door on a seven-floor building, then roof-hopping several buildings in search of the guy is too awesome to not mention.
Shado taking out several of Fyers' goons, and beating him unconscious, with her bare hands.
Roy holding the flechette that Ollie used to save him while the lights in the club go red. Epic foreshadowing is epic.
After force-feeding Oliver concentrated Vertigo,, the villain mocks Oliver, and says he doubts Oliver could aim a single arrow. So he fires three. One which hits the bad guy dead in the heart.
Diggle pulling a Big Damn Heroes moment, and kicking multitudes of Mook ass. Even finishing one off with a defibrillator shock to the head.
"City of Heroes", the Season 2 premiere, shows that the writers will keep giving us awesome moments:
Island!Ollie showing some good moves while sparring against Slade.
Laurel disarming one of the copycat Hoods.
Felicity nailing one of the copycats with a piece of wood in an attempt to distract them from killing Ollie.
Roy beating two copycats at Verdant, even if they do manage to kidnap Thea.
The return of Arrow. Ollie appears in costume in only one scene in this episode, but what a scene: he singlehandedly defeats all four copycats without killing themto save Thea. Seems that this other way works well for now.
A non-fighting one: Walter showing up, as CFO of Starling's National Bank, to buy Queen Consolidated's remaining shares, ensuring that Isabel Rochev doesn't take control of the company.
Finally, when Ollie says he doesn't want to be called the Hood, Diggle asks him what he does want to be called. He holds up a green arrow and the camera focuses on it, then cuts to the title card. It's not at all subtle, but it's just awesome!
There's the opening scene, with Roy taking on the Triad by himself. He totals his car, bangs himself up and gets arrested, but he took out one of the bikers and held off the other.
Later, Arrow and Diggle vs. White and Tiger; Ollie shows that you don't need a kill shot to take someone out, and Dig reminds us that he can hold his own against China. And when she attempts a Break Them by Talking rant against Arrow, saying that he'll never be seen as anything but a criminal, he shoots her downbeautifully:
"As long as this city is safe, it doesn't matter."
Felicity sending the whole SCPD task force on a wild goose chase after the Arrow by hacking into their video feeds with year-old surveillance.
A minor one for both characters involved is Roy hearing something suspicious behind him and accurately throwing his flechette, only for the Arrow to casually catch it, then tell Roy that you don't need to beat up bad guys to be a hero, offering to let him be a spy and scout in the Glades.
Finally, though it was a pretty cruel move, Laurel setting up a police sting to catch the Arrow was admittedly impressive for her.
Black Canary, pinned under a pile of metal rods, kills the Dollmaker and disappears in the space of a few spoken words. And before that, her Big Damn Heroes/Dynamic Entry at the very start of the episode, crashing down through the ceiling and wielding her sonic device against the cops to stop them from capturing Oliver.
The Reveal at the end where it would appear that Black Canary (and by extension Malcolm, going by what he said last season and by the messenger's Dark Archer outfit) was trained by none other then The Demon's Head himself, Ra's Al Ghul.
Finally, our vigilante is called the Arrow for the first time in-universe! And Lance gets to coin the new name.
Arrow and Black Canary (who thought Oliver would have told her family that she was alive) fighting side by side in a true Battle Couple moment against the hired goons of "The Mayor", and it finishes with them using each other's own Weapon of Choice right after Oliver had taken out a grenade with his arrow.
"League of Assassins":
The various fights against Al-Owal and the League.
Round 1: Ollie and Sara barely defeat Al-Owal, before he gets away.
Round 2: The Arrow and the Canary barely escaping with their lives against three members of the League.
Round 3: Sara faces Al-Owal and his two minions in the clock tower, which she has booby-trapped Skyfall-style. She ends up defeating them with the Arrow and Quentin's help; the latter kills a ninja with his spare gun, she kills Al-Owal, and they spare the last one to send Ra's Al Ghul a message: Leave the Lance family alone.
Al-Owal performs an Arrow Catch... with an arrow shot at him from behind.
Quentin deserves credit for deducing that Sara is the Black Canary after only talking to her for a few minutes.
"Keep Your Enemies Closer":
Ollie and Diggle not only breaking into a Russian gulag, but breaking back out. Credit for an assist goes to Felicity, who designed the compact explosive hidden in a red star to look like a piece of Soviet kitsch.
Diggle proving just how honorable he is by letting Deadshot go despite having a clear shot at him, because that was the deal he made.
A world-class hitman and a special forces Battle Butler decide to work together to escape from the worst prison in Russia. Cue the ass-kicking.
"State v. Queen":
Malcolm's Wham Shot of an entrance, leading to The Reveal he wasn't dead AND he still hadn't lost his aim. Not to mention him casually telling Moira that he bought off the jury to her trial, releasing her from being in jail — oh, and The Reveal that Thea is his daughter.
Even though it breaks his one rule, Oliver, not as Arrow, putting an end to Count Vertigo by shooting him in the chest with three arrows, the force of which sends him falling to his death.
Thanks to one mention of Nanda Parbat, Moira manages to contact the League of Assassins and inform them that Malcolm is still alive, ensuring he'll be too busy running away from Ra's Al Ghul to reveal to Thea that he is her father. To truly emphasize how awesome this is, upon hearing Moira speak the name Ra's Al Ghul, the smug smirk that seems to be Malcolm's default facial expression vanishes and all he can ask is how Moira knows that name.
Barry trying his hand at guessing things about the Arrow... and actually is pretty Awesome by Analysis. Along side, Felicity of all people, who gets more and more edgy. And then he starts to describe her.
Barry: So you've seen him, right? The Vigilante? I read that he saved you. What was he like?
Felicity: (beat) Green.
Barry:Green. That's interesting, right? I mean, why green? Black would be better for stealth and urban camouflage. Me, personally? I think that he trained in some sort of like, forest or jungle environment. And the green is a nod to that.
Barry: Do you wanna know something else? I think that he has partners. Definitely someone with a background in computer sciences.
Felicity: (Guiltily moves towards her computer babies)
The Arrow's fights against Cyrus Gold/the Acolyte, who's been injected with the Mirakuru serum, giving him superhuman strength and durability. Ollie loses both fights, but he more than holds his own. Also, he reveals that he has defeated another Mirakuru user while on the island.
Felicity coming up with a plan to save Oliver from an unknown substance and being discovered by the public when Diggle, second best Team Arrow tactician couldn't. Drafting Barry Allen to help figure out the solution that has been injected into Oliver, by revealing their secret to him. Since she's the only one who really spent anytime with Barry, she both knows he's pro-Vigilante and has a strong enough relationship with him that even if he wasn't, he probably still wouldn't reveal her secret, ipso facto (thank you, Count) not being able to reveal Oliver's.
Barry going right up to Ollie: "And you don't have to thank me, but you should thank her instead of being kind of a jerk." Especially considering that the first thing that Ollie did upon waking up is strangle him and threaten to kill him.
Barry shows off more Awesomeness by Analysis, managing to figure out what's wrong with Ollie and cure him in a matter of minutes. He then reveals that he went to the trouble of getting the oils off Ollie's neck so they can recreate fingerprints of his attacker.
Oliver getting over his survivor's guilt thanks to an hallucination of Tommy, who encourages him to get up and fight, and defeating Cyrus Gold by shooting the centrifuge full of Mirakuru, that spills on him and probably kills him.
And before he does that Oliver fights Gold and pretty much demolishes him in close combat, and this is the guy who kicked him into a ceiling not long ago.
The comic-based Deathstroke, Slade Wilson, complete with eyepatch, superpowers and some white hair, is in town, is the man behind Brother Blood, and wants to make Ollie suffer before killing him.
Also, superpowered Slade making a demonstration of his new abilities combined to his skills, easily killing three of Ivo's men and breaking a rifle.
The particle accelerator goes haywire in a storm, killing the power in the process; Barry gets up to close the skylight in his very wet lab to brace for the storm. And then things start going strange: the chemicals start responding to something; time seems to slow. He looks up, and in a great flash of yellow light, he gets struck by impossible lightning. There is something oddly satisfying in finally seeing the creation of Barry's super powers, and despite how traumatic it may be, you know awesome is soon to follow.
Barry making this for Oliver. And when Oliver wears it for the first time (seen here)...