I voted for the SNES era, as it has the most nostalgia for me. Since I'm really bored right now, I'm gonna type a bit about all of them in the series, 'cause I like to hear myself talk/type. :P
Gameboy Series:
I never played any of them, so I know nothing about them. c'est la vie.
FF: Mystic Quest
This was my very first Final fantasy RPG, and very well may have been my first RPG ever. (I'm not sure just where Dragon Warrior I fell into the timeline) I know everyone frowns upon this game, and I do also, but way back in Elementary school, this game was actually pretty neat.
Final Fantasy I:
This was the third FF game that I ever played/owned. I even still have the official Nintendo Power strategy guide for it. Issue #17. haha The game was definitely pretty advanced for its time (When compared to Dragon Warrior I, the only real competition around at the time). I've beaten it a few times over the years.
Final Fantasy II:
I only ever gave this game a real shot when I bought the anthology PSX CDs. I never beat it, but I did get a good ways into the game, and I still play it on occasion. I trained the shit out of my characters as soon as I got Ming Wu, or whatever his name is, so I had like 5xxx HP and 1xxx MP. So it's really just a matter of tearing through the storyline to beat it. Interesting leveling system, but I wasn't a huge fan.
Final Fantasy III:
By far the best game of the NES era. Not only were the graphics a lot better in terms of towns and shit, but it also started the whole secrets and subquests idea in FF games. Items hidden in random patches of grass, secret areas, and being able to change your job. Very sweet. I never got too far into it, though, as all I have is a ROM for it. I wish they'd re-release it, like they did the others.
Final Fantasy IV:
Reinheld pretty much summed up my thoughts on this game. It was my first true FF game, and I thought Rydia was the fucking bomb. I know that it's not the best game in the series, nor even in the SNES era, but it was the one that really got me hooked, and I have to give it props for that. Just a very solid game, through and through.
Final Fantasy V:
I went through this game once. I liked it. The idea of changing jobs was neat. The graphics were identical to FFIV, which gave it points, due to the nostalgia I had for FFIV.
Final Fantasy VI:
Arguably the best FF game out there. The storyline was great, the characters were neat, the graphics were beautiful (For its time), and its music kicked ass. As corny as it sounds, I still like to listen to .mp3s of the music at times. It's the FF game that I have started up the most times, usually to try and do some completest thing, like getting all rages. Admittingly, I always end up stopping, as I get kinda bored when it turns into the World of Ruin.
Final Fantasy VII:
FFVII was a good game, but I think it gets more credit than others in the series, simply because it was the first FF RPG for a lot of current gamers. That being said, a lot of the music is neat, and the game was fun to play. The characters sucked, though, as it started the whole trend for having cookie-cutter characters that were all identical except for moves they did as limits. (i.e. There was no "mage" no "fighter" no "healer" it was basically just materia.)
Final Fantasy VIII:
I hated the magic system with a passion. Seriously, WTF... I don't know what they were thinking. But one thing is for sure, FFVIII had the most kick-ass music of any of the FF games, I think. Again, we saw the generic 3-person setup, where the only thing that differed between them was their appearance and a move they could only use every now and then... More cookie-cutter characters. I beat it once.
Final Fantasy IX:
I only played this game once, but I did enjoy it quite a bit. In my opinion, it was like a SNES RPG with PSX graphics. The characters were not cookie-cutter, as each character had a different abilities that were unique to them. The storyline was neat, and the characters were enjoyable. It also paid homage to all previous final fantasy games, by incorporating aspects of each and every one into it. I think it was a really neat game.
Final Fantasy X:
No walking around on the world map... what the fuck?

I did not like that aspect of the game at all. It was kind of neat how all the zones were directly connected, but still... We're talking the PS2. They could have really flexed some graphical muscle in making a kick-ass world map, and all they gave us was a picture with some lame airship graphic that let you choose locations to land on. The sphere system for gaining levels was pretty neat. It kept the characters for being cookie-cutter unless you really spent a shitload of time leveling them up to traverse them through the entire sphere grid. Great graphics, movies and music, though. Blitzball blew.
Final Fantasy X-2:
I think baby jesus cried when the Japanese came up with this game. Charlie's Angels meets Final Fantasy meets a 14-year-old Japanese Schoolgirl. Super lame dialog that made you embarrassed to play the game with the volume on your TV louder than 5 aside, the game had some enjoyable aspects. Haven't beat it.
Final Fantasy XI:
My first MMORPG. I love the fact that you can freely change between your jobs, while keeping your character name, as well as things like fame, items and money. On the other hand, a lot of aspects of the game were tedious that made it hard for you to want to do them a 2nd time, or 3rd, or 4th. I still think it was a fun game, and I can respect people for sticking with it. The end game, however, was just not my cup of tea, and always needing to rely on other people to accomplish any task got old.
So yah... I grew up with final fantasy games. They are my favorite RPG series, and I have always purchased consoles based upon which ones Squaresoft went to. (With the exception of N64, since that game had crazy-fun 4-person party games.) I'm a pretty old-school gamer, though, so I'd have to say that the SNES ones were my favorite for the combination of old-school graphics and play style and stuff.