This whole thread is spoilery, so don't even preview if you're not ready!
Mine would have to be about halfway through the game, when you fight Barthandelus for the first time. The party is like "okay cool, time to fight this Jihl lady. No? I guess the pope dude wants to fi--oh. Oh god." and all the while Fighting Fate is kicking in.
Another silly one worth mentioning is near the beginning after the Vestige is wrecked. Snow wants to stay with Sarah, but Lightning is like "no PSICOM is coming we'll all die" and suddenly Vanille interrupts with "UH OH. Let's~ run away? Ciao!" and then she does this little Cactuar pose and skitters off.