Basch's final duel with Gabranth and Balthier repairing the Bahamut and piloting it away from Rabanastre, respectively, are probably the best.
Fran reacting violently to the Mist while captured. After convulsing in pain, she then, after letting out a terrifying scream contrary to her reserved, subtle nature, proceeds to tear the Imperial guard trying to hold her down a new one by flipping on them with claws and jumping off each other rapidly single-handedly.
Fran also gets a special mention for not being held up as a sex symbol depending on how you interpret it, despite her clothing...or lack of it.
In the Pharos:
Ashe: Rasler. My prince. Our time was short. Yet I know this: (raises her voice) You were not the kind to take base revenge! I am no false saint for you to use! In all Dalmasca's history, not once did we rely on the Dusk Shard. Our people resolved never to use it, though their need might be dire. (sighs) That was the Dalmasca I wanted back.
The princess who spent most of the game ready to commit a MacGuffin induced genocide by nuke against the empire decided to defy the will of the gods and her own desire for revenge and become truly, completely, heroic.
Vaan telling Gabranth, the man who murdered his brother in cold blood, how revenge is pointless. He's saying this to the man who murdered his guardian and forced him to live on the streets for two years.
And then, at the very end of the game:
Venat: They are fulfilled beyond your knowing. The Cryst is sundered, age of Stones complete. From the undying ones the world is freed. You shall not tread this path alone. Together we go. Come.
Until this point, it was amibigous Venat was an ally or a Manipulative Bastard toward Vayne and Cid, but then, while it would have been easy to him/her to leave and abandon Vayne who asked for it, The renegate Occuria chooses to stay and die alongside his remaining ally definitely prooves that he/she really respected Vayne and Cid and was truly an idealist ready to give up its immortality for humanities freedom we then learn that the bad guys were a legitimate Nakama, and we get a very rare exemple of a Rousing Speech given by the last boss who know he/she will not survive this, but accept his/her death anyway because he/she feels that his/her role is fulfilled: now, making a game when the player can respect the villains for more than being sexy is quite a feat.
Also, Judge Zargabaath's redemption for his earlier failures in the game's closing act. It proves unnecessary, but it was a damn heroic sentiment.
It helps that he's voiced by Simon Templeman, who plays Kain in the Legacy of Kain series, a game series renowned for it's voice acting. And anyone who's played those games knows that his voice exudes awesome.
"I Judge Magister, condemn you to oblivion!"
Larsa's comes when after defending Vayne for the whole game, Larsa finally sees that his brother has gone off the deep end and stands up to him. "Though I lack your power, I will still persist."
Gabranth turning against Vayne, charging him, impaling him, and saying "Even a stray has pride."
Before that, we had Vayne Hulking Out of Manufacted Nethicite, and an injured Gabranth dragging himself onto the scene. Vayne tells him to protect Larsa while he deals with your party. He looks at Larsa, who is lying unconcious on the ground, and at Vayne who is standing above him spewing magic everywhere. Then, he points his sword at Vayne, and comes out with the most awesome line "Yes, I will protect Lord Larsa".
Vaan picking up one of Gabranth's swords, charging Vayne, and mortally wounding him in the process. Impressive considering how early in the story arc his character arc was resolved.
There's more than a few, notably Balthier's Hovercycle escape, but if any stands out, it would have to be Balthier and Cid, atop the Pharos at Ridorana. It's the sort of scene you can watch again and again, undoubtedly silly but still so awesome.
Any scene involving a Judge Magister, or them talking and debating with each other. Few and far between though.
What and Reddas going out by basically taking a tactical nuke to the face to save the party and atone for Nabudis isn't epic enough? The people in Balfonheim who knew him even called it a so-so death for him. A so-so death?! How epic is this guy if what's basically a tactical nuke to the face is only a so-so death?!
Going to throw in another for Vaan. When they reach Eruyt Village the Viera are all ignoring you and basically telling you to piss off. Vaan's response paraphrased? "I don't care what you want". He then proceeds to continue browbeating them until they finally give in. Even Balthier admits that he didn't think they would get anything out of the Viera.
More awesomely, once it is revealed the Viera don't care about Mjrn any more because she left their village, he then points out that pointing them in the right direction will see them gone as well, and so they are all better off if the Viera help them. He didn't so much pester them as manipulate them into helping.
Judge Drace gets one when she attempts to strike down Vayne for the murder of his father, even when Bergan informs her that by doing so, she is raising her sword against the army itself. Even though the scene leads to Bergan effortlessly throwing her aside and Gabranth being forced to execute her so that he might stay in Vayne's service to protect Larsa, it's still pretty awesome. She gets even more awesome when rather than protesting her fate, she calmly orders Gabranth to get on with it while extracting a promise from him to protect Larsa.
The Shiva exploding after Ghis tests the Dusk Shard by sticking it in the ship's drive. Awesome in that "wrath of God" type way.
Judge Bergan's insane and truly awesome rant against the Gods and the Power of Man as he stands over the corpse of Ivalice's High Kiltias. His delivery is simply glorious and the voice actor is having a ball hamming it up with oozing theatricality. The boss fight that follows is disappointingly easy, but the scene and the monologue itself are some of the best writing this series has ever had.