1. Timeless classic, but a bit simplistic and dated compared to what came after. Recommend playing (or emulating) the PSP version.
2. Very dark, depressing story. Rather inconsistent difficulty. Even cheating by quickly raising party levels at the beginning by grinding and having them beat each other up, and making the dangerous journey to Mysidia as soon as possible to get some of the best spells, some dangerous bosses can be 1-hit killed with the frog or warp spell and many random encounters will instantly hand your butt to you. Recommend playing (or emulating) the PSP version.
3. Introduced the Job system, which is one of the best aspects of the franchise. Takes days of mindless grinding to get the job mastery certificates and Legendary Smith equipment and to max out levels if you want to beat the Iron Giant. Recommend the Steam version.
4 and After Years. The best jumping-on point for newbies to the franchise. Dark and depressing story, but also beautiful and hopeful. Heartmeltingly beautiful musical score. The DS and Steam versions rebalanced most abilities (it's shocking, but Edward is actually useful!) and the Augment system allows brilliantly customizable gameplay and creative strategies. But to my great shame, to this day, I haven't been able to defeat Proto-Babil. Alas, the Lunar challenge dungeon and Interlude chapter from the PSP version are missing in the Steam release.
5. My personal favorite. Best storyline and gameplay mechanics. The only thing 6 does better is the musical score. Play on Steam.
6. Only slightly lesser than 5, except the music. 6's soundtrack is Uematsu-sama's greatest achievement. The remastered Steam version is okay, but a bit lazy with letterboxing and the mouse cursor visible in fullscreen mode and the hideous made-for-touchscreen interface, and breaking Windgod Gau and PsychoCyan was unforgivable. Emulate the GBA version.
7. Overrated. Confusing, bizarre story (especially when reconciling with Crisis Core, Before Crisis, Advent Children, and Dirge of Cerberus), pointless, badly-implemented mandatory minigames breaking the flow. Brilliant graphics for the day, but debatably haven't aged well. But the Steam and PS4 versions update the graphics reasonably well, and on PC, you can mod it to use more modern, Advent Children-like models. The Steam version forces you to sign up for a separate account with Square's website, which is BS.
8. Flawed, but still great. Underrated, I say. The leveling and magic systems are overly complex and punish you for leveling up, to discourage grinding. The story is beautiful, if a bit weird. Ignore that "Spoony" fellow's rants.
9. The best of the PSX-era. It's Sakaguchi's personal favorite. A loving tribute to 1-6. My only complaint is the chibi-models. If only it used realistic-proportioned models like 8, it would be a perfect 10.
10 and 10-2. The voiceacting is actually good, but badly-matched to mouth movements. Jaw-droppingly beautiful visuals (especially in the remastred International versions.) Unfortunately, there's less emphasis on exploring and discovery, with fast traveling between areas being the norm. The return of the Job system is brilliant, even if used mainly for fanservice costume changes.
11. There's an 11?
12. Don't bother with the original. Wait for Zodiac Age to come to steam.

Everything after 12 is crap. Except War of the Lions, I guess.

I personally enjoyed XIII-XV, with the best probably being XIV. The other two weren't really all that good, but they were enjoyable in the end, and both did things well imo.

edit. And now I'm just noticing Zodiac Age is being released on Steam tomorrow. Yaysies!