It depends on how many of them you want to play. If you want only the best, play 6-10 and you're done. You've got the best story, the best characters, the best gameplay and the best combat/customization nailed already. Any of the other titles will be lacking one or more of these - particularly after 10, when they started sacrificing big in the character and gameplay department to make more room for flashy visuals.
11 and 14 are MMOs, and both are pretty bad. 12 and 13 are also pretty bad; flashy with no content. 13 is uniformly bad, from start to finish; you're thrown into a linear hallway and that's literally the rest of the game. 12 starts off like it might be an epic adventure worthy of the ages, but instead you follow a kid as he follows around slightly more interesting characters (who are still not very interesting) on *their* quest to do... things. Mostly you just run around from set piece to set piece, with token betrayals and boss fights coming and going with no feeling of connection or emotion.
Somehow they decided that 13 was worthy of sequelage, and both of those are worse than the first (if you can believe it).
The early games are uniformly better than the tripe that came after 10, but going too early leads you into the fairly simplistic 80s RPG sprite-focused gameplay. FF1, 2 and 3 are pretty interchangeable with very token plots and characters who often don't have a personality at all. 4 has characters with names and a hilarious attempt at a love triangle, but it falls short as none of the characters are terribly likeable and the rotating door cast that fills the rest of your team is either forgettable or outright annoying. If you have any interest in playing FF3 or 4, get the DS ports (or android/iOS releases, which are the same thing). They're the highest quality release of those particular titles. They aren't bad, per se, they're just... not anything special, especially by today's standards of RPG.
5 is alright. The story, again, is very token, but the characters finally start having a "point." They have enough memorable lines and enough of a "human" element to begin to really attach to them, and the cast being kept relatively small lets each one get some story focus. The class selection in 5 is mindboggling, and you get a ton of different (and neat) options. Some are trash, unfortunately, but you're sure to find something you like. There's a small level of customization (you can take an ability from another class, etc) but nothing on what the next 3 games offer. 5 is decent, certainly not bad, but not the best of the best, either.
6 starts the era of greatness. It features a rather large list of characters, many of whom get incredible amounts of background story and great arcs throughout the game. Some of the later-joining characters (particularly the joke ones like the Mime) arrive too late to be meaningful to the story, but the rest of the characters will have you very invested. This is also the game where the music started taking off - there's even a scene at an opera, featuring an opera song, which is easily the single best piece of video game music *ever written* [http://www.youtube.com/watch?v=cOcmdymYws4]. And, of course, it's also meaningful for the characters involved. Beautiful game (for the time), if you can find it on PS1 it comes with some extra cutscenes, otherwise the GBA port has the best translations and quite a few bug fixes over the old versions. 6 is highly recommended.
7 continues the era, applying the same amount of character focus to a 3d world. No longer clinging to sprites, cutscenes with facial expressions and easily-detectable body language help flesh out each member of your team. One of the best elements of the story is the villain, Sephiroth, who I assume you've heard of. He's not a random bad guy that just pops out of nowhere - he's present from the very beginning of the story until the end of it, sometimes as an idol, sometimes a hated villain, and the things he does will make you WANT to kill him as much as any video game character can. At the same time, his motives are somewhat believable, if a little far-fetched - he's not just a mindless freak who wants to destroy the earth (like, say, Kefka in FF6). He's dangerous and intelligent, and the game builds up to the confrontation at the end flawlessly. Do not miss this game.
(On a side note, FF7 and 8 are tied for the best combat/most customizable characters. The Materia system featured in 7 offered nearly unlimited possibilities, ranging from dedicated damage summoner to pure melee fighter to anything in between, and the addition of counter-attack materias, MP/HP steal materias, and various other neat supports will keep you entertained for the whole game, with a very steady stream of new materia even until the end of the game, ensuring you always have something new to try).
8 is a contentious one, but mostly follows on from 7 in tone. The graphics are again improved, being the first game to actually feature "human-like" characters instead of random polygon blobs. The characterization suffers slightly, only focusing on a small group (and even then, only on a few of that group specifically). A somewhat confusing side plot emerges, there's some shenanigans with time travel, and the game's biggest flaw; the villain isn't really built up like Sephiroth or Kefka. You don't have an entire game to just *HATE* this character for what they've done. You barely even know who they are, and then when it's time for the final confrontation, you're just going through the motions. Yeah, it's a boss, you're supposed to kill it... but who really cares when you're not invested in the fight?
That said, the rest of the game is still superb. 8 offered a slew of hard-to-figure-out side quests, some with incredible awards; a few summonable espers hidden away in side areas, and like I mentioned above, some of the best combat customization in the series. Each esper has a set list of abilities it grants to the person who has it equipped; those abilities are a mix of universal and unique skills, some passive, some active. You can even customize them to a great extent by deleting some of the universal abilities (the Summon command, for example, is on every one and doesn't need to be) and adding some of your choice. It's not *quite* as much freedom as 7, particularly considering 7's sometimes-convoluted summoning chains, but it's certainly a hell of a lot better than most of the final fantasies. Don't miss 8.
9 is a hidden gem - it came out after 7 and 8, also on the PS1, but it was released so close to the launch of PS2 (and thus FFX) that it didn't get much attention. It plays almost like a light-hearted parody of earlier final fantasies; not a serious, gritty save-the-world adventure but still good in its own way. Some of the best minigames in the whole series can be found in 9. Definitely recommended... after the other "greats."
10 is the last one I'd venture to call "good." The drop in quality is obvious, but considering how legendary the previous 3 games were, it's still head and shoulders above a lot of competing games, especially for the time. It's a very pretty game (starting the trend of sacrificing overall quality for shiny objects) but the addition of voice acting was... stupid, to say the least. Only a few characters have voices that "match" their person and also don't suck. Both the leads have some of the worst voice actors possible; not just during the infamous "laughing" scene (don't look it up, it's painful) but throughout the whole game. Yuna is the mumbling queen and Tidus is the confused dipshit.
The biggest problem is that this doesn't actually mesh with their characters. Tidus starts off as a confused dipshit, but quickly matures in the face of constant danger and a quest to save the planet. As truths are revealed about the last stages of their journey, Tidus sobers up, transforming from a confused and bratty teenager into a responsible, caring (but still somewhat naive) young adult. The transformation is subtle, but quite good - many people who quit playing before the end miss it, which is unfortunate. The voice actor, however, never got the memo, and Tidus sounds like a cockbag from start to finish. Yuna's is even worse, not following her arc, but even during moments of severe distress or anger, never rising above a quiet inside voice. Tidus manages to yell a few times, Yuna just mumbles. It's a fucking disgrace. I'd read the text any day and imagine voice actors of a much higher caliber. Sticking them in and doing it poorly was just a mistake.
The combat is an interesting mix of menu-driven turn-based and "real time," and it's very easy to get into. The class customization (in the NA version) is equally easy; there isn't any. You're put on a fairly linear path through the sphere grid, forcing characters to pick up their archetype abilities in order and only being able to break out of the path very late in the game. The "endgame" content is also rubbish; very grindy, forcing you to catch 10 of every monster ever then battle a special, souped-up version of it in the arena. 99% of these fights are just a test of whether you have Quick Hit on every character or not. If not, you lose. Snore.
The story, somewhat like 8's, is contentious. Personally I loved it. It's got the fairly common japanese anti-religion theme, but it goes deeper - multiple characters even in your party face off against each other in arguments and debates. As the story progresses and more is learned about the church and those who run it, the cognitive dissonance of previously certain characters is evident. They've been raised their entire lives to believe XYZ, and now that it's proven to be a wrong, how do they deal with it? Certainly interesting stuff.
From there, though, the quality drops drastically. X-2 starts off with a pop song and continues through a boring and strangely samey grind through the world X took place in, just with all the interesting characters benched or off-screen for the majority of the game. FF12 couldn't come near the characterization evident in 6-10, and 13 wasn't even trying. Those shiny hallways couldn't design themselves, you know?
