Thought of some more:
Yuffie: GAWD! If had known this would happen, I'd have taken rope escape lessons more seriously!
Elena: That's the will and spirit of the Turks! Believe it!
Cid: Welcome aboard, numbskulls!
Reno: A pro isn't someone who sacrifices himself for his job. That's just a fool.
Cid: Hold onto your drawers and don't piss in 'em!
Vincent: As long as she is happy... I do not mind.
Red XIII: I am the son of the warrior, Seto! I'll see to what's happening to the planet! And I'll return a warrior true to that noble name!
Cloud: Come, planet! Show us your dreams! And Sephiroth! To the settling of everything!
Tifa: You really did come when I was in trouble!
Cid's speech on the Highwind about protecting the planet and him spoiling it by saying he hasn't thought of what to do yet. I always found that scene full of feels and humor both and liked it for that. Also, when Elmyra chews out Barret for leaving Marlene alone. She really ripped into him, and it'll be interesting to see how that plays out in the remake. Oh and Tifa's reaction upon realizing that the others saw her and Cloud under the Highwind the night before the last battle is priceless, that should be quite a moment to see in the remake, too. She'll probably be red as a tomato when that happens.