Hmm...I don't know if these are the *best* moments but I think they're my favorite out of the games I've played:

FF6: (SPOILER)The scene where Locke gets the Phoenix esper, (SPOILER)the scene with Cyan and his family after the events on the Phantom Train, (SPOILER)the scene before the final battle

FF7: (SPOILER)the scene where Tifa helps Cloud remember who he really is, (SPOILER)the scene where you find out Sephiroth's killed everyone in Shinra hq

FF8: (SPOILER)the scene where Squall carries Rinoa over the FH bridge and...telepathically talks to her or something...it was cute , basically the whole end

FF10: the ending...favorite one out of all the FFs I've played

FF10-2: um, the ending again... (SPOILER)Good version

FF12: the beginning , (SPOILER)the scene at the top of Pharos, the ending