The big thing someone touched on was "first FF they played". A trend I noticed among newer JRPG gamers is that Final Fantasy usually brings them into the genre, and the first one they play is often their favorite. Lately, this is anywhere from FF7 to FFX.
Now, me, I've been playing since the original Final Fantasy on the NES, and those like me just simply don't play Final Fantasy anymore. I think FF8 is what killed it for me. FF9 and FF10 had fun enough gameplay, but the stories were incredibly lackluster. FF8 was just pathetic on all accounts. The only FF I've ever played I couldn't finish (well, I got rid of FF3 on the DS before I finished, but honestly, it bored me. It didn't pain me like FF8 did, either).
Now, at the same time, my distortion of the FF quality has also been messed around with. Before 7, all I had was FF1, 4 and 6. If I had also played 2, 3 and 5, I would've seen that the majority of titles released were, in the end, plain old good but nothing fantastic. As it was, America got the best of the series. FF1 is still fun to this day, containing a ton of elements forgotten. Let's not forget challenge. FF4 was the first video game any console gamer played with a seriously good story. Even Cecil, who used to be the angstiest hero of them all, dealt with his issues in a relatively mature manner without the bullshit. Final Fantasy 6, well, that story is just flat out amazing. The gameplay was fun for the time, though at this point a bit boring. Nonetheless, Magicite was probably the best "everyone can use magic" system they've implemented, and even then every character class still had a purpose.
With that in mind, FF7 was also a big step. Firstly, it was the first title to not be censored. It's also the adult of the games, oddly enough. In any case, it also introduced a lot of new ideas to Final Fantasy, while simultaneously providing a "complex" story. Now that I'm older, I can look back and say "y'know, that story wasn't so amazing after all", but at the time it really was awesome. Also, EVERYONE knows Aeris dies now, but back then it was still a big shocker. Even as messed up as Cloud was, he at least didn't whine like Squall did, either. FF7 also threw in a shit ton of "mini games" like snowboarding, bike riding and other such things that they pulled out of the development of Mario RPG. This variety throughout the game actually added some nice fun.
Now, ultimately, FF7 was certainly not as great storywise as FF6's, though I have to say I prefer the gameplay of 7 more. So, I can fully understand people clamoring for either FF6 or FF7. However, any title after that I just blame on ignorance. Anyone that favors a Final Fantasy after either of those just hasn't gotten to truly experience the evolution of the JRPG genre, knowing what is trite and what genuinely works, or is simply illiterate in that they haven't experienced much in the way of truly good stories.
To those people, I say either read Dune or Memory, Sorrow and Thorn. Each of these book series has teenagers start out as the main "heroes", but they make every other teenage hero that is so popular in RPG's today look like the retarted, recycled ideas they've always been. Especially Paul Atreides. He's just bad ass.