Ike: Then we will fight... and we will save our people. Make your peace with whatever the gods worship. The end is near.
Soon after, he proceeds to (with good goddess Yune's power) deliver the final blow and kill a god. Complete with Ass Kicking Pose.
In Path of Radiance Marcia, whose older brother Makalov's debts, gambling, and general Scrappyness had caused her to quit her job, fight pirates, and fly all over the country to try to find him. And what does she say to him when she finally finds him and he pathetically tries to talk his way out of it? "STUFF IT, SPONGE-BRAIN!!! NO MORE LAME EXCUSES!!! FOLLOW ME!!! NOW!!!"
Marcia also has a scene where she intends to fight off an entire troop of wyvern knights by herself to protect Elincia, Leanne. and Nealuchi (a queen, princess, and princess' royal retainer respectively), and spouts a constant stream of insults at them the entire time. She even manages to yell at Haar in the midst of the battle to make him help her.
Elincia in Radiant Dawnhas the confidence to lay down her weapon in between two warring armies just to prove a point.
"I just need to pull this axe out of my head here... Whooo, that's sharp!"
Naesala's first appearance in PoR, or saving Leanne and Nealuchi from Skrimir...
Sanaki's conversation with a certain subordinate near the end of the game... Doubles as a Funny Moment.
"You are my subordinate, after all. I've decided that leaving one's empress to die is punishable by drowning in a pool of rancid butter...I hope you're a strong swimmer."
Leanne is the cause of one when she arrives in Crimea in Part 2 of Radiant Dawn. Paraphrasing the narration: "The Crimean nobles don't like how Elincia welcomes the Heron Princess to court so readily, but they know that if they say anything Tibarn and Naesala will tear them apart, so they shut up about it."
The end of Part 2, involving The Greil Mercenaries' Big Damn Heroes moment to rescue Lucia from execution.
Kurthnaga's Big Damn Heroes moment at the end of 3-13, levelling a castle with a single attack to provoke a ceasefire.
Vantage combined with Wrath and Resolve. Basically, if a character has all of these skills and ends up in a really bad situation, they turn into a One-Man Army.
Whenever a heron manages to get a kill in Radiant Dawn with a magic card.
Soren gets a few:
Repeatedly mouthing off at the battle-thirsty lion laguz general and future king of the beast tribe Skrimir, knowing that the latter respects him and can't win the war without him.
If he fights Micaiah during Part 3, chapter 7, he outright insults her. Note that everyone she meets loves her within moments of first talking to her, or at least treats her with much more sympathy than her actions elicit, and he Meteors her. In the face. Usually twice. Best yet, performing this Moment of Awesome is one of the steps to unlocking a secret ending scene.
Soren: "Do not presume to understand me, you ridiculous girl."
Soren essentially makes all the strategic decisions in relation to Ike's army, which means he has a direct hand in bringing down Ashnard, his own father.
He gets a big one in his backstory. He manages to find someone he has only seen once in his life who didn't even stay in the same country, by himself, as a little boy. Both for the resolve to see it through, and the fact that it actually worked.
When Leanne and Reyson restore the forest by singing.
And to make this scene even more awesome? His comments about the event to Ike later in the game in their Level B Support conversation:
Reyson: When I bashed Duke Tanas's face, he only suffered a bloody nose, but it cracked the bones in the back of my hand.
Ike: ...But it felt good, right?
Reyson: Oh, yeah.
Radiant Dawn also managed to do one via an elaborate bait and switch. You spend most of the first two parts of the game controlling Micaiah's efforts with the Dawn Brigade and Elincia's attempt to keep ahold of her throne, respectively. And while you see a lot of familiar faces, there's several questions at times about where Ike and the Greil Mercenaries are, as Elincia would ask for their help if she could find them. In the end, she deals with it on her terms, captures the traitorous Duke Ludvick, and imprisons him, only for him to try to talk his way out of it by trying to ransom off Elincia's foster sister and bodyguard Lucia, who he'd captured earlier, by literally presenting her ready to be hanged outside the walls of Elincia's castle. To accept is to doom her authority as Queen of Crimea for all time, but to refuse is to condemn Lucia, her closest friend, to death. Everyone knows this and even Lucia tells Elincia not to throw everything away for her sake. Elincia doesn't, and is about to watch Lucia die for her...when the Greil Mercenaries show up out of nowhere, save Lucia, proceed to trash Ludveck's remaining forces around the scaffolding, and generally remind everyone just why they were the badasses that helped win the last war in a brilliant introductory moment that wouldn't have worked half as well if they'd been there from day one.
The sequence as a whole is a Moment of Awesome for Lucia. The poor battered-looking young woman remains defiant to the end as she declares her loyalty to Elincia moments before she is to be hanged. Lucia's response to Elincia's decision to sacrifice her for the good of the country? "Hah!"
Similarly, the scene beforehand is a Moment of Awesome for Elincia as a queen, because she made the hard choice to let Lucia die not knowing all of this was about to happen.
Haar: Why couldn't you just stay on patrol? Saw a pretty little heron and just had to have her, is that it? I could never decide if you were more greedy or more corrupt. Stupid was never in the question, though. Zeffren: Who do you think you are?! You're a traitor, just like Shiharam! The dracoknights spit on your name! Haar: ... Do they now? Well, here's your chance to try the real thing.
How about the fact that once he becomes a dragonlord (which can happen on the last part of the second chapter), he ends up nigh on invincible. topped off with about a 30% chance of unleashing stun (3X damage and paralysis), plus huge strength, defence and killer axe, he kills all in seconds... whilst half-asleep.
Haar is so awesome that when he re-recruits Jill in the midst of a heated battle where they are on opposite sides, she's swooning near the end of his speech.
Haar's conversation with Levail in the Tower of Guidance gives Moments of Awesome for both of them.
Levail: He is the last true knight. I will die for him. Haar: Yes, Levail. You will. Levail: How I dreamed of fighting a proper foe! I am honoured, Sir Haar! Have at you!
Tauroneo's exchange with the Mad King Ashnard is a brilliant and particularly poignant illustration of the man's character and is severely reminiscent of General Duessel, the Obsidian, from The Sacred Stones.
Ashnard: Is that you, Tauroneo? As I thought... You betrayed me after all.
Ashnard: In my father's time, there was a man who was one of the Four Steadfast Riders. That man grew old and useless, and retired from the front lines. How does his story end, you ask? Come, let us write it together.
Tauroneo: Oh, my king... In all of Daein's history, perhaps no other ruler has used the talents at his command to the degree you have... But all the same, no other king has chosen a path so incredibly stupid.
Ashnard: Heh heh heh... Will history judge me to be just or evil? We will not know until all of this is finished.
Tauroneo: ...Now that I've confronted you and traded words with you, I have come to a decision. Throughout Daein, I, Tauroneo, will be known as the king killer. Come! Let me earn my name!
When Lucia and Bastian have resigned to leaving Geoffrey behind as a decoy, Elincia refuses to stand for it. Lucia orders Ike to lead Elincia to safety, and he adamantly refuses. His reasoning? He still has a contract with Elincia personally as a mercenary, and is thus insistent upon doing the mission to save Geoffrey that even Geoffrey himself and his own sister believe is not worth it. The fact that Elincia and Geoffrey can get married in the sequel makes it well worth his trouble.
Sothe getting promoted to Whisper by Yune. He seriously says he feels great- so great he could arm wrestle with Skrimir.
Most of the boss dialogues in Part 4, especially against Izuka.
Bastian outright says he would to dissect Izuka's brain to find a possible cure for Renning.
They also save plenty of choice words against Lekain.
Sanaki: Burn, traitor!
Elincia's amazing Rousing Speech before assault on Ashnard's palace is both this and a Heartwarming Moment. Especially when you consider how quiet she was throughout the entire game. Even Ranulf was impressed!
If you decide this way, Ike can give one as well. It's shorter, but just as awesome.