Any time a particularly well-timed Dual Strike or Support Block occurs can make you want to cheer.
Better yet, if you're lucky enough when facing a particularly tough enemy, you may be able to see a Dual Strike with two critical hits. Pairing up a Dual Strike with two of the better crit quotes makes it even more awesome.
Or if speed allows for two strikes from the attacking unit...and then the supporting one Dual Strikes twice. Almost makes you feel bad for the other guy.
The mechanics behind the Swordmaster skill Astra mean that, if a Dual Guard takes place on the initial strike, it will also happen for the other slashes during that attack. This means that the supporting unit makes the Dual Guard roll, it's possible that they'll be Taking the Bullet for their partner not once, not twice, but five, ten, fifteen, or TWENTY times in a row (the latter requiring the enemy to have a Brave weapon, go second against a foe slow enough that they'd attack twice normally), proc Astra every single attack), without taking a scratch. Even if they're a Priest or Mage, and only have cloth robes protecting them. BADASS.
Once the villains get big enough to have their own crit and Mastery skill quotes, you can get excellent exchanges. Nothing counters Validar's "this was all written" quite like Chrom's "anything can change."
Once characters start unlocking their Mastery Skills, max out their stats, and Pair Up with someone they have a high support with (especially if they're married), just about any single battle has a good chance of becoming this.
The entirety of the exchange between Cassius and Kjelle in Kjelle's recruitment paralogue. HAVE THEM FIGHT. You will be treated to the following:
Kjelle: If you believe in any gods, you'd better pray to them now!
Cassius: My, my. Aren't we confident?
Kjelle: I don't fear you, coward!
Cassius: Aye, I suppose not. Most fools assume that liars and sneaks like me are weak. They want us to be weak, see? They NEED it. It lets them hold on to the fantasy that right prevails in the end. Heh... They can think what they want. A cocky fool is an easy target. Truth is, in the end, it's the clever ones who always survive.
Cassius: Wrong, girl. Your master will have COMPANY!
Walhart, of all people, gives a pretty epic verbal smackdown to Raydrik if you have the two talk in the DLC Rogues and Redeemers 2. In summary, Raydrik suggests the two of them team up to take over the land, and Walhart responds with "And Then What?", and when he sees Raydrik hit an utter mental brick wall, he calls him pathetic, and that without vision, a conqueror he is not. And then he finishes it off with saying that a schoolyard bully with a stick could dream up greater ambitions than him.
Beat Rogues and Redeemers 3, and Ike will say that he's never fought anyone half as strong as you. This coming from a man who fought (and beat) Ashera, half of the creator of the universe.
The icing on the cake is Grima's reaction. Seeing this incredibly cruel and evil demon once so smug in his invincibility and incredible power begin to visibly panic in fear of knowing he's going to die for real is very satisfying.
Bonus points if Avatar scores a critical when fighting Grima. "Checkmate!" is of course the best one, since it could be the blow that wins the whole game for you, but even simple lines like "Here's how it's done!" suddenly take on new meaning against the Avatar's Evil Counterpart.
"You're finished!" is also incredibly fitting for the situation.
This troper's fight against Grima with the Pair Up unit of Robin and Chrom, resulting in two Dual Strikes and four crits, ending the fight on the first turn with the most perfect possible critical quotes for the situation. To say that it was an absolutely epic way to end the game is a severe understatement.
Chrom: Anything can change!
Robin: Here's how it's done!
Chrom: Your end has come!
Scoring a critical with either Chrom or Lucina. "Anything can change!" and "Hope will never die!" are spot-on for the moment.
It gets absolutely hilarious if Frederick hits a crit on Grima, telling a god himself to "Pick a god and pray!" And very badass, too.
Even better, after recruiting them through the Bonus Box, the player can deploy every SINGLE lord from the previous games to fight alongside Chrom. While none of them speak, it feels pretty damn awesome to fight the embodiment of evil alongside characters like Sigurd, Lyn and Ike.
And then at the end there's a triple crowner, and since that in itself is awesome, it most fits here. After you beat Grima for good and your allies start expressing confidence that the Avatar will return, Lissa delivers this gem:
Lissa: You're right! He/She has to be out there somewhere... And we'll find a way to bring him/her home. Even if we have to search every open field in this whole stupid world!
Sadly offscreen, Lon'qu defending Lissa from a random band of assassins (including archers) single handedly during their A support, which is an impressive feat even when you're controlling him in battle.
There's a surprising number of "action-y" supports in this game, such as:
Female Avatar and Aversa escaping from a group of assassins by working together, in one of their supports.
Sumia refuses to let go of the beehive she found for herself and Gaius even when the bees have stung her all over, because she wants to help him to get honey that badly. Gaius, who until then was comically hostile to her, is extremely impressed by her Plucky Girl nature, and ends up giving her all the honey inside.
Noire, one of the frailest characters in-story, manages to give Yarne enough inspiration and courage to become mentally and emotionally stronger. We're talking about a shy Ill Girl who is seen as a mix of Fragile Flower and Lovable Coward most of the time, but her A Support with him oozesSilk Hiding Steel and shows that she does not always need to relay on her Split Personality to get things done.
Yarne: You're fighting in the next battle?
Noire: I am.
Yarne: ...Ah. I see.
Noire: For all my faults, the others still trust me enough to rely on me...
Yarne: But aren't you scared?
Noire: Of course I am! Even now, my hands are shaking...
Yarne: Then why force yourself? Wouldn't it be easier to just stay here andó
Noire: It would, but I don't want to do what's easy. I want to do what's right... Yarne, if you don't want to fight, you don't have to. I won't judge you. I don't want to go out there either.
Yarne: Then why go?!
Noire: B-because we have to win this war, and it's time for me to make a stand! So, yeah. I'm scared, but I'm going.
Henry's marriage proposal to Sumia is both this and a Crowning Moment of Funny, not to mention damn creative. What's best than proposing to the girl you like by switching bodies with her both to ride her pegasus AND to get her a perfectly fitting wedding ring?
The Plan of the Avatar as revealed in Chapter 23 is incredibly awesome.
The Avatar then proceeds to blast Validar with Thoron, shutting him up.
Give the bad guy a a round of applause as well not Validar, but the Hierophant, who reveals himself/herself to be Grima from the Bad Future, who was able to take the Avatar as a host and followed Lucina to the past, and even though he wasn't able to possess the new Avatar, he was able to manipulate events just enough to use the Hierophant as a sacrifice to revive himself.
The Avatar's rather philosophical speech in Chapter 14, in which he tells Chrom that people aren't controlled by fate, but instead walk their own paths in life, strengthened by the invisible ties between them and others. Particularly good if you're playing a Male Avatar and have already achieved an A Rank Support with Chrom, as it comes across as something of a Meaningful Echo of the speech Chrom gave to the Avatar in that support.
Morgan also says something similar to his/her non-Avatar parent, suggesting that the Avatar still believed in those words even in the future. Though which future is up for debate, given Morgan's unknown origins.
Emmeryn, who put the badass back in Badass Pacifist. Her back story alone is incredible. Not only did she ascend to the throne at the age of nine, but she undid her father's ugly legacy of religious genocide and turned Ylisse into the most beloved and peaceful nation on the continent. Let alone that in-game, she's absolutely fearless. Going back to a war-torn nation where her capture is nigh-inevitable, because she won't abandon the people she worked so hard to protect? Sacrificing herself to stop the entire ruling bloodline of her nation from being captured or killed? Emmeryn will do all that and more, and not even flinch.
Furthermore, consider that in Paralogue 20, girls from the village she's been staying at have been abducted. Emmeryn is one of them, but escapes and this is after stepping off the cliff and sustaining brain damage.
The Future Past 3 gives the possessed Avatar one. S/he continues to fight from the inside to prevent Grima from slaughtering Lucina and her friends, even after Grima insists that his/her spirit has been completely consumed.
Noire's introduction is downright fabulous. She begins in captivity by slave traders and stripped of her weapons, but as soon as she finds a bow & arrow, she undergoes a Split Personality Takeover and starts mowing down her captors like a crazy mofo!
Even better is how there are several flying units on the map, so Noire not only gets to attack her captors, she gets to hit many of them For Massive Damage. Too bad for them they had to imprison an archer, huh?
Tiki's recruitment Paralogue is this, since it's one of the few missions in the game where the enemy can easily back you into a corner even on Normal due to the fact that it is an Escort Mission, where you have to defeat every enemy while preventing them from killing the defenseless Tiki. What makes it harder than most other Escort Missions in FE is that the enemies will completely ignore you unless there's no other way to get to Tiki, and enemy reinforcements just keep on coming for several waves from all around you. By the end, it's perfectly possible to be seeing a huge mess of Risen surrounding your army as you hold them back as best you can while you wonder when in Naga's name will they tire of throwing themselves at you.
While some of the bonus paralogues fit into other categories, Paralogue 19: Irreconcilable Paths, is this in spades' A battle at a rain-swept promontory at the edge of the world map against enemies strong enough to actually challenge overlevelled characters (which you will probably have several of by now). Topping it off is the fight against Walhart who when fought in the main storyline was somewhat underwhelming after all the hype surrounding him. Here, he's far stronger (quite possibly on par with the final boss depending on difficulty) and gives an epic rant on his motives and beliefs before battling you, not to mention the fact that he has forced some of the strongest of the Risen (Lucina even remarks that they are on par with those of the Bad Future when Grima was at full power) to bow before his will. The only thing able to top this is the fact that if defeated correctly he joins your army, complete with unique class, weapon and a very good statline.
Henry, if he's Owain's father, gets a big one in their B-Support. After taking an arrow to the shoulder protecting Owain, he and Owain realize that they're surrounded. Henry tells Owain to run and says that he himself will stay behind to take care of it. Which he promptly does, with the implication that he absolutely tears his opponents apart, considering the wound he took for Owain before the battle is the only one he suffers. But what makes this stand out is the fact this scene is entirely unique to Henry. Every other potential father — the Avatar and Lon'qunote Who, remember, fought off an ambush of archers to save Lissa in their A-Support. included! — flee the scene with Owain; they tell him that it's an ambush, they're surrounded, and that they both have to run. Henry is the only father who was deemed powerful enough to take on an entire ambush on his own, while injured, and win.