Cecil's fight with his own inner darkness to become a paladin turns him from a depressed, unsure knight into a confident, walking engine of physical destruction, ready to fight for his beliefs instead of letting himself be forced to do nasty things against his will. Incidentally, the easiest way to win that fight is awesomeness in itself: sit there and take the hits, paying penance for what Cecil did as a Dark Knight.
Not only that, she shows up when Cecil is the only party member still standing, meaning that she's protecting him- just as he protected her from Baron's soldiers at the beginning of the game. It just doesn't get any better than this.
And for a villainous moment, when the heroes confront the Fiend of Fire, Rubicante, he actually apologizes to Hot BloodedNinja Edge that his Mad Scientist assistant tortured Edge's parents and turned them into monsters sent to fight him. He then proceeds to completely heal the party before fighting them because to do otherwise would be unfair. He gets another in his final defeat, where he praises Cecil and companions for successfully defeating him once more.
Before his final defeat he deviates from many villains by appearing with the other elemental lords and telling you that (unlike other villains who merely try to outnumber you in an ambush) they have learned the power of team work from your past victories and proceed to fight you as a team.
That's more due to technical limitations. Having four bosses on the screen would be impossible even in the DS version. The spirit of the dialog clearly indicates that they're fighting together, even if the game doesn't show it.
The Four Fiends may fight one at a time, but you are given no chance to save or heal outside of battle until all four are defeated at once.
This troper's favorite moment in the game was the assault on the Giant of Bab-il. The entire armies of the world, with every bit of technology and magic at their aid, assault the Big Bad's ultimate weapon. So. Much. Awesome.
Edge, speaking to Rubicante in the Tower of Bab-il, especially in the DS version. As Rubicante gives a pitying speech about how Mankind is a slave to their emotions and can never know true strength, Edge instantly slips into a Unstoppable Rage and delivers an awesome line to Rubicante amid a swirling storm of lightning.
Edge: "You think our rage... a weakness? Then let me show you HOW WRONG YOU ARE!!"
The two instances the "Theme of Final Fantasy" plays. It's not Awesome Music for nothing.
The summoning of the Lunar Whale. The awesome music accompanying the scene is nothing short of epic.
Cecil calls out to Golbez in the finale, calling him his brother. In the original, Golbez merely turns around to say farewell; in the DS version, we see him as Theodore as he says goodbye. It's much more effective if you're used to the original version.
After Cecil's inexplicable "Stay in the Kitchen" abandonment of Rosa and Rydia on Earth before the final battle, they show up once he lands on the moon, having apparently been clinging to the outside of the Lunar Whale during its trip through space. Utterly ridiculous, but nobody cares.
They weren't clinging to the outside, they were sitting in the entrance chute.