Well, I'm currently on this mission. I've played and beaten (in the numbered series) 1,4,5,6,7,8,9,X,X-2, and 12. I actually just finished FFIV DS yesterday!
*Note: the following are my opinions, not fact, except, uh, when I just list facts

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I will agree with Magnus that the stories are a little generic, but the cool thing is that each entry has its own unique way of telling the story.
FFI is the simplest of them and you can probably beat it within the 10-20 hour range. You pick nameless heroes, name them, and give them classes. You are the Light Warriors and you are on a quest to save the Crystals. That's about the gist of the story. I would go with the GBA version. My NES version is glitchy.
FFIV is my favorite game in the series and has some actual character development. Each character has his/her own backstory and personality as opposed to the nameless heroes of FFI. I have 4 versions of this game and my favorite is the GBA version. The SNES version is the easiest, the PSX version uses more foul language than it needs to, plus requires you to be around LV 60 to beat the game, and the DS version is the hardest of the bunch. Cecil was on level 75 when I beat the game and I still had a tough time with the final boss. Plus, a lot of the bosses are just plain cheap, and it took me over 35 hours to beat it. I was just trying to run through the game without doing a lot of extras! The GBA version's difficulty is in-between the SNES and PSX versions, has the best translation, (the DS version was a little too far on the "proper language" side of things for my taste, but it was also a solid translation and the only version that has voice acting that is actually quite good) and has the most extra features. It took me just over 20 hours to beat the GBA version and Cecil was on LV 55.
FFV is decent. It gives you 5 characters that are fairly well developed, but the overall gist of the story is predictable and the main villian is known early without a major plot twist. FFV is more about character customization and stat buliding than about storytelling. As you progress through the game you find new jobs (warrior, black mage, etc.), which you can assign to your characters outside of battle. Any character can become a master of any job. There are some good story points and most of them involve Galuf.

The final boss is the most disappointing of all the FF games I have played and the ending is probably the worst. Still, despite its bad points, it is still a good game. I've only played and beaten the GBA version and it took me 38 hours on the dot and my characters were in the high 40s. My PSX version went on the fritz.
FFVI is one of the strongest in the series. It doesn't have a central character per say, but it has a strong cast of characters. Most of the characters have strong motivations for being in the party. Like V, there is plenty of room for character customization but the set classes return, like only Locke can steal and so forth. The main villian is actually intriguing and takes a big step forward from the lame-o bad guy in V. I have only beaten the SNES version and I'm not sure how long it took me. It was probably in 35-45 range, but there are ways to beat it faster and slower than than 35 hours.
FFVII is the now the overexposed and probably now one of the most over-hyped games in history. It is a solid game and was graphically revolutionary in 1997. All the characters have backstories and good development as the game progresses. My major turn-off to this game is the profanity. I just don't like reading it. It uses the materia system to give your characters magic and special ablities. Every character can master every materia, but one character can't learn another's limit break. The two leads of the game, Cloud and Sephiroth, have been over-exposed and now suffer from either fanboyism or scorn. I was playing it through again when I realised that the writing and character motivations are better than the haters would want you to think. I would say that if you play this game, try to do so without thinking too much about what others say about it - there is just either so much love or hate for this game now that it is hard to find a middle voice. It takes around 40-50 hours to complete on average.
FFVIII is my least favorite game in the series. This game has more problems than redeeming qualities. Only 3 characters get any sort of development - the others are just kind of there. You have to draw magic spells from the enemy monsters and then junction that to your stats. Like, if you draw a 100 fire spells and junction that to you strength, you will hit harder and so forth. If you cast magic that is junctioned, you lose that magic and your stats will decrease. With the exception of a few spells, magic is generally useless anyway, but you still have to draw it to improve your stats, and you have to train these things called Guardian Forces (or GFs) to learn things like "Junction Defense" and so forth. The magic draw system is time consuming and boring. The story doesn't make a lot of sense and says a lot for a fantasy game.

The cinematics are quite nice and the music is enjoyable. (check out FINAL FANTASY VIII - Fithos Lusec Wecos Vinosec on iTunes, one of my favorite albums ever) The game does a good job of what it really wants to do, which is to tell the love story of Squall and Rinoa, but it does so at the sacrifice of well, everything else. I've beaten it once.
FFIX moves away from the more futuristic settings of VII and VIII and returns to the the more fantasy settings of the series youth. It is considered by many to be the sequel of FFI. Your characters learn ablites by equiping certain, uh equipment.

Not every character can learn every skill and it generally doesn't take that long to learn a skill. There are execptions though. The game's story makes more sense and the love story part of it was central but it doesn't take away from the other characters, which is one of FFVIII's fatal flaws. The story has dark moments but has many lighted hearted ones as well. It has a whole bunch of little scenes that are usually just comic relief. The challenge is moderate in most places but can be hard or easy depending on what skills you choose to learn. I've beaten this one a few times and it takes around 40-50 hours if you take the time to enjoy the game. There are ways to reach the end of the game in less than 6 hours, but I have no idea how to do that, nor do I really want to.
FFX is good game as well. There isn't a major plot-twist, but the story it has is told well. It is the third game in the series in a row that has a romantic relationship as a central plot point, so you may not want to play 8-10 in a row or your romance meter may explode.

Anyway, the battle system is a little different from the other games in the series that I have played. The GBA version of FFI as well as every other FF game that I have played (except XII) runs on the ATB system, in which your characters can move based on time gauges and the enemy can continue to attack while your gauges are filling up. In X, everything moves in a set order based on speed. The setup can been seen at all times looks like this: (sort of

)
X = Character 1
Y = Character 2
Z = Enemy 1
A = Charater 3
etc.
When it is character 1's turn, you are given C1's menu and everything else stops. You can then select the action you want to take at your leisure and can leave the game alone without pausing it. It's still a fairly fast paced game and it is nice to know exactly when the enemy will move, but it does take away the fast thinking that you have to do in a FFIV, for instance, especially if you set the enemies to active which means that they will continue to attack even when you are in a menu. Instead of leveling up, your characters move through the sphere grid as the gain sphere points, which are earned by winning battles. Every character starts on their own sphere path, but if you wanted to turn Tidus into a mage and Yuna into a warrior, you could statwise. I wouldn't but you can.

Only Yuna can summon and equip staves, Tidus can equip short swords only, and so forth, but every character can learn every spell and attack, except for each other's limit breaks and summons. It is also the first game in the series that uses voice acting. The voice talent is usually quite good, but there are moments that make you cringe and it suffers the same fate of every dubbed game: the voices don't match the characters mouths. A small quibble. The characters themselves are memorable but they are not the deepest characters ever either. Overall, FFX is a solid game and can be beaten fairly easily as long as you don't run away from most random encounters as you progress. I'm not sure about time, but usually within the 40-50 range, though you can take 100 and still not have everything done.
X-2 is the Charlie's Angel's FF. The story is campy overall, although some of the side quests take a walk down the darkside. The job system of FFV returns, except now you can change your job mid-battle. When you change your job during a battle you get to watch a Sailor Moon esque transformation scene and then the character says a one-liner that is related to the job. You can turn those off if you want. Also, ATB returns! If you don't do the side quests, the game is really easy. I think I beat it in less than 20 hours the first time, but you can play the game in excess of 100 hours and still not have all the jobs mastered and still not find all the games secrets. It also has a new game+ feature. What you get out of this game depends on what you put into it. To sum up, main quest easy, side quests moderate to hard. If you don't play X, I wouldn't bother with X-2.
Lastly, FFXII. This game suffers storywise because it takes a few cues from VIII. A couple of characters are fleshed out well and are compelling, while some of the others are ignored. However, the characters they do focus on, especially Balthier, are really cool. The characters level up normally, but learn skills from the license board. When you learn a skill the skills around it become available. Any character can learn any or all skills, except for limit breaks because those are character specific. You wander around like in an MMORPG and fight monsters in that way, but with a FF twist. You control only one character and the other 2 act on AI commands that you give them. You can also give your party members direct commands at anytime, in case they start doing something stupid. The plot is one of political intrigue, though you can probably guess what will happen early on and be right. I'm not a big fan of XII. It has some good elements, but what is frustrating about the game is the lack of money. If you want money, you have to steal items from monsters and then sell them for money. Most items don't go for a lot money so you will be desprate for cash the entire game and since you have to buy most of good equipment in the game (for a lot of moola) you will find yourself fighting a lot just to get enough bread to buy things. (I re-read that sentence and I didn't like how many times I saw the word "money." Synonyms rock!

) I also don't like the battle system itself - it just dosen't feel like a FF game to me. The voice acting is soild overall (Balthier is awesome

) and the music is pretty good. It took me 60 hours to beat the game.
I guess that Revenant Wings is actually XII-2, but I have only played about an hour of that game. It is a RTS and I was having a fairly good time, but I don't have further info. My brother says it is a game you beat once and never play again.
Never played XI, and I started II and III but never got very far.
Well, that's my take and brief insights into the games of the FF series. I really like the FF series and I think most are worthwhile gaming experiences.
I would recommend:
FFI - its where the series started and it is not overly long. I based my thoughts on the GBA version.
FFIV - soild story, memorable characters, soild game play, you don't have to overly level your pary to beat the game. I would go with the GBA version, though it does have slight lag.
FFVI - soild story, memorable characters, soild game play, you don't have to overly level your pary to beat the game. That looks familiar.

SNES and PSX versions are the same, except that the PSX version has extras that don't really affect the game itself.
FFVII - try not to be swayed too much from all the overexposure this game has suffered as well as benefited from. Form your own opinion.

FFIX - soild story, light hearted characters (to go along with several of the darker characters), and just a fun experience in general. The dialogue is really clever.
FFX - fun but some of the voice acting can make you gag on occasion. There are also several side quests you can go on to extend the game.
FFX-2: if you beat X, you will see why there was an outcry for a sequel. A really campy game but still fun. I would play just to hear Paine's one liners.

I don't know your play history with the FF series, but I really started with IV and I would recommend you start with that one as well. The game is linear and you will never get lost, and it covers most of the mechanics of all the other FF games. After that, feel free to try any of the games in the series. I would play VIII again only because I would want to hear the games music in context.
I hope that helps.
(Wow, that took a long time to type.

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