No lie, Aeris' death was the first time I actually sobbed to a video game... like, real bad.
I never sobbed, but it was the first time a characters death actually meant anything. It's difficult to truly care about characters whose only way of emoting is cartoonish symbols popping up over their heads.
VII was the first game I ever played where two characters could have a conversation in a beautiful environment, have it develop their characters, and have it be effectual enough to be taken seriously. I don't think it was particularly well written, especially by other mediums standards, but no other game - not any entry in Final Fantasy beforehand - had a scene like the slide scene outside of Sector 7 that actually worked.
That, and I think superficially Final Fantasy VII has some of the best JRPG mechanics. Battle is crisp and satisfying, Materia is accessible and deep enough that customizing your characters for battle is a lot less tiresome and grind-heavy as the previous job systems. It's atmospheric in a way that only a handful of other games are - and none in the Final Fantasy series.