Oh boy, where to begin...
Final Fantasy All in all an entertaining game despite becoming a bit dated. I'd recommend playing this one simply because it's a classic if nothing more. The battle system still stands up as entertaining but how to progress in the game can become a bit confusing every now and then.
Final Fantasy II It gets a lot of criticism for abandoning the level system but I think it's a very good stat system. Basically, the more you use skills, the more they improve. The main issue is the HP exploit which involves you attacking your own party members until near death, healing them and repeating. In terms of story, a big improvement over the first game. I'd recommend it.
Final Fantasy III I found this to be one of the more tedious of the early games, the job system was a potentially cool idea but I just didn't like the results. I also wasn't a fan of the story as I prepare to have more personalised characters. Although to the games credit, the DS version had an actual cast of characters rather than four generic Onion Knights.
Final Fantasy IV I haven't played.
Final Fantasy V I haven't played.
Final Fantasy VI Without a doubt my favourite of the sprite-based games that I've played. It has a large cast which have very diverse personalities and great personal journeys. The battle system is fun to play and the Magicite system remains one of my favourite ways of learning spells and increasing stats. The overall story is very gripping and entertaining. What I will say is that the second half of the game (no spoilers) is a drop in quality until the final boss which is an enjoyable fight.
Final Fantasy VII I've only played the first couple of hours of it but I was very entertained by it, it's one I intend on revisiting and completing. The materia system was one that I found to be very intriguing. The characters are for the most part very likeable, there are two that I found to be very dull but otherwise a great cast.
Final Fantasy VIII My favourite game despite how it divides the fanbase. The cast were great and Squall's development throughout the game solidified him as one of my favourite protagonists ever. The Junction system was a good idea but could be exploited easily early on which makes the difficulty of the game questionable. If you're playing for story, then jump straight into this one.
Final Fantasy IX A game with a lot of potential but failed to hold my attention. I also intend on revisiting this one at some point and seeing if it changes my mind.
Final Fantasy X Possibly the second most loved of the Final Fantasy games (behind VII) and for good reasons. It removed the world map feature which was a massive change and went for a more linear approach but it still managed to have great side quests. The main plot gets a bit messy and contrived in places but in the end it pays off. The characters are great although people complain that Tidus is whiny. I disagree, he complains every now and then but if you play the game you'll know that he has a damn good reason to.
Final Fantasy XI Avoid it, the game is unbelievably tedious and dull. I'm sure it was a lot more fun when there were lots of people to socialise with but now the world is fairly empty.
Final Fantasy XII The game got off to a very strong start for me but about five hours in I got bored. The protagonist, Vaan, is possibly the worst of the Final Fantasy leads that aren't custom characters. Basch, one of the other primary characters would have been a much stronger lead. The story isn't very clear initially but as you go on you get more interested, the world itself is what bored me after a while. Outside of Rabanastre, the world isn't interesting.
Final Fantasy XIII One of the least popular games among long-time fans because of how different it was. It's my second favourite of the games though as once you get into it, you fall in love with the characters, the world and even the battle system. The battle system was derided as "the game plays itself" but that's simply not the case at all, as you go on you find that there's a lot in timing and strategy. The side missions later in the game can be ridiculously tough if you don't know the system in and out. The game was indeed very linear but once you reach about two thirds into the game you get a chance for a large amount of free roaming which was very welcome. Play it.
Final Fantasy XIV Haven't played it, don't intend on playing it.
My personal ranking of the top three would be: FFVIII, FFXIII, FFX or FFVI. I have a lot of trouble deciding between FFX and FFVI.