When the cast discovers that the world will end 1000 years after they were born. Them, their children, their grandchildren, their great-grandchildren don't have to worry about it. Is it somebody else's problem? ....hell no. They can travel through time, that Eldritch Abomination is going down.
The moment Frog opens the Magic Cave. Sure, you had to give him a pretty big push. But from that point on, he is nothing short of a true hero.
This doesn't really do the scene justice. After recovering and repairing the Masamune, you take it to the cave that Magus' troops use to move around. He stops and listens, inspecting the blank cliff face, and has a flashback to himself and Cyrus. Then, he turns, takes the Masamune, and his theme begins to blare. A sudden pulse of light surrounds Frog, before shooting into the sky, and then he spins around and slices the mountain in half.
Marle gets one in a sidequest. Her father is about to be convicted unjustly by the Evil Chancellor. She's locked out of the courtroom, despite having found evidence to prove his innocence. What does she do? Breaks through the stained glass window into the courtroom, bails her father out, and kicks the shit out of the so-called Chancellor.
The whole series of events of bringing back Crono from the dead, storming the Black Omen, and fighting Queen Zeal and Lavos in the final battle to decide the fate of the future makes for one hell of a climax.
If Magus is in your party during the second Zeal fight, his battle theme overrides the one that should normally play, making the showdown all the more awesome especially since he's her son and she's too far gone to recognize him, as well as the lines he says.
To be fair, Schala didn't recognize him either. The only person who recognized him as Janus was Gaspar.
Schala recognizes him in the DS version's extra ending, but it doesn't do much good.
Any boss battle where the "secondary" boss theme plays, such as Black Tyranno. The song that lets you know that this boss isn't like the bosses you've been fighting, this one's gonna pound you.
The battle with Heckran, as soon as you realize you're fighting the guy on the cover.
And all of the Anime Scenes in the PS version. You can only do so much with sprites, but the full on animation shows the glory that could only be implied in those same scenes. Special mention goes to the scene with Frog, now you see the elements under his command (even Crono is bracing himself against the wind) as he cleaves the mountain in two.
Early on, when Marle is sucked into a void and nobody has any idea where she went, Crono walks right up, grabs her pendant, and volunteers to rescue a girl he just met. Why? He's just that much of a Bad Ass.
Playing around on a New Game+ is awesome. It gets repetitive after a while, but going back through the game - through all those bosses that gave you so much trouble - and absolutely curbstomping everything is great fun.
When Frog at last takes up the Masamune and slices it through ten feet of stone, opening the entrance to the cave leading to Magus' castle.
Whatever opinion you have about the PSX re-release, you cannot deny that the anime scene of that is epic. Behold.
Crono's is when, battered and defeated, he walks straight up to the mouth of the creature that just decimated both his party and the previous Big Bad, and would eventually destroy the world. In spite of everything he uses his last ounce of strength to challenge Lavos one more time before being vaporized.
The entire party gets one of these when they finally confront Lavos and have to psyche themselves up, although Ayla, Marle, and Lucca's are the best: "Ayla strong! Ayla and world good! You outsider. No part of planet's life!!" "This is Crono's and ours...Leene's and Doan's...everyone's...and I mean, EVERYONE's world!!" "Impossible... You CAN'T expect to toy with an entire world and get away with it!"
Lavos gets to respond via the Time Devourer in Chrono Cross, and is absolutely pissed that a bunch of livestock (Seeing as he essentially bred humans for his own purposes) dared to kill him in what he seems to consider a grievous case of Carnivore Confusion. If they can get to declare him evil just because he happens kill them as part of his spawning process, then to hell with it, he'll stop people from being able to hurt lesser animals through eating and living themselves, by ending all of time. That'll show those hypocritical bastards. Seeing as this is about the only thing that Lavos/Time Devourer openly states in the entirety of the series, it's funny how often that bit gets glossed over.
Marle's jump-through-the-platestained-glass-window moment during the King's Trial Side Quest definitely deserves mention.
Practically everything Magus says or does, with highlights included below:
When the party first confronts him, his theme music begins playing, and he prefaces the fight with this line, with the song hitting only moments after the fight begins:
Magus: The black wind blows... All right, give me your best shot... If you are prepared for the void!
"If history is to change, let it change! If the world is to perish, let it perish! If my fate is to die, I must simply laugh! I'm coming, Lavos!"
What he says if you have him in your party when you fight Queen Zeal, his mother.
The first time you meet Ayla, she challenges you to a Drinking Contest for a Plot Coupon. The next morning, your Gate Key is missing, so she joins up with you to storm a nearby Reptite lair to get it back. Once you get it back, she sinks to her knees and... throws up. How awesome is she? She can whip the ass of an entire race of hyperintelligent dinosaurs... while hung over.
Maybe so, maybe no... given the rather blatant hinting that Kino and Ayla give the party before departing at the end of the game, it seems that Ayla might not have been hung over, but suffering from morning sickness. Still pretty badass, though... helping save the world whilst pregnant.