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.