For me the most Iconic moment of Final Fantasy is where I finally get my hands on Final Fantasy XIII for the first time, like a month ago. It's the one moment that I really glad it really happened. I've been of Final Fantasy XIII for about 2 years or more, I don't know. But only able to play it about a month ago.

But if I need to say about in-game iconic moments,

FFVII : (SPOILER)where Tifa needs to find Cloud when he's out of his mind. Bike mini game, (SPOILER)not the one in Gold Saucer, but when being chased by giant robot thing. and the last : (SPOILER)Caith Sith sacrifice scene.
FFVIII : Dancing scene, Date scene (SPOILER)somehow I can't get to have a good date with Rinoa. and the last The Ending scene (SPOILER)not after the battle, but the CG ones. I can't understand how could they survived from that place. Then suddenly got back to Balamb Garden for CG scenes. Like what happened after Squal meet Edea for the last time?
FFX : The Turn-based battle system, Kimahri smile scene, The Ending.
I haven't beaten Final Fantasy X-2 yet. But I give one iconic moment FFX-2 : The return of ATB system
Also I haven't beaten Final Fantasy XII, so for now just one iconic moment FFXII : The return of open world Final Fantasy also the battle system is quite unique.
As for Final Fantasy XIII, Final Fantasy XIII-2 and Lightning returns, I haven't beaten them. I want to write the most of the most iconic moment of each game
But this is my opinion