I'm a ex-jrpg addicted (still recovering ) and a long time fan of the Final Fantasy series. I have played all the games on the series except XI. What I can say is that it's a great video game franchise, packing 20 years of (mostly) great games. So what about them? Let's see....

I and II... Dragon Quest clones, unless you want to feel nostalgic and/or frustrated (the original FFI and FFII for the NES are incredibly hard) avoid them. The remakes suck.

III. After the DS remake it's worthwile. It's weak on story as it's other two NES companions, but is the first game with a more complex job system.

IV. The true beginning of the series. The first game to really tell a story (a great one to boot) with great characters. FFIV was the game that made the series avantgarde in comparison to Dragon Quest, Phantasy Star and other old jrpg franchises. Try to play the original japanese translated, it's better than any remake or the US SNES localization. Failing that, play FFIV Advance.

Mystic Quest. Ignore this.

V. Return of the job system. Weak story. Poor characters. It's a upgraded FFIII and a step back from FFIV. Avoid it.

VI. Great, great game. The start of the "high-tech" Final Fantasy. FFVI is cyberpunkesque, has a great story that starts cliched (evil empire against good resistance, yay) but builds up and becomes really impressive. Also, Kefka owns. It was my first FF. Also, the last game of the series actively directed by the series mastermind Hinorobu Sakaguchi. Play it.

VII. Terribly overrated, but great game even so. VII is the game that not only changed the series, but changed video gaming by having a major role on giving dominance to Sony. VII has a good system and a good story, play it when you have time.

Tactics. Best game in the series. Play it. Enjoy it.

V III. Love or hate case. FFVIII takes what VI and VII accomplished and takes it to the next level. It's very hi-tech, has a great, but very complex, story, great characters and a GREAT system. Try it. If you end up hating it, you are not alone.

IX. Well, my 2 CP on it. To me FFIX is a good game, but has lot's of wasted potential. The only character that really develops and is rich is Vivi.
Good system, but a little too simple and shallow compared to the junction system. It's very nostalgic though as it recapture the old (pre-VI) FF feel.

X. Good. FFX has a good story, good characters and a system that rivals the junction on depth. It's very big, full of frustrating side quests, however terribly linear up until the very end. Still have the dreaded random battles... sigh. Play it if you have a PS2.

XI. Not played. Seems that it's old age makes it suffer against World of Warcraft. Well, I don't like MMORPGs anyway.

Tactics Advance. Very good. Has a system better than the legendary Final Fantasy Tactics, but weaker story.

X-2. Stay away from this.

XII. GREAT. Really great game. From Matsuno and the team behind Tactics. It's actually the only FF to feel high-fantasy, even with some amazing technology mixed up in the middle. However, the protagonist is useless to the story, and the story is actually much greater than the characters, making them feel small and shallow for the most part. The system is not what junction or sphere grid were, but it's fairly good anyway. Finally the end of random battles on the main franchise after 11 years since Chrono Trigger taught the lesson. Play it. It's worth buying the PS2 for it.

VII Spin Offs. They suck, don't play them.