I've played I, II, IV, V, VI, X, XII and XV. VII, IX and XIII are still on my list of games to play eventually, maybe VIII if I'm ever in the mood.
I initially skipped VII because it is just too popular, I already know the entire story - including sequels, prequels and the movie. IX kept crashing on my PC and XIII wouldn't even run - I'm still waiting for a collection on any console I own.
As for the ones I've played, X is the best one hands down. It is incredibly flawed, but still my favorite. The gameplay is the best in the entire series, I actually never liked the ATB even on wait. Instead we've got a great dynamic turn system and the constant swapping of party members was a great addition. The entire party felt useful. I also think the sphere grid is the best level up system in Final Fantasy. It has a great story too, although the really interesting bits about Sin aren't actually explained a lot, instead we waste an enormous amount of time on Seymour who I found utterly boring in comparison. Other than that, X's biggest flaws are Blitzball and the Cloister of Trials - both of which are so clunky, they kept me from completing the game more than once.
From the pixel era, I think VI is the best one - mostly because of it's story. Followed by IV and V. However, I like all of the games I played despite the implementation of the ATB or whatever you'd even call II.
Lastly, I think both XII and especially XV get a bad rep they don't necessarily deserve. I quite enjoyed them despite their flaws. My biggest gripe with XII is that the game plays itself after you've programmed your team, especially with the speed-up button modern versions have. There wasn't much gameplay in my second half. XV honestly only suffers from being too fragmented, half the story is hidden in movies, comics, animations and such. Other than that, I really came to like it once I accepted its action gameplay. I'd even call it my second favorite game overall and would like another game with the same system. (It may be noteworthy that I played XV completely blind, I only looked at trailers and the development history after I finished it.)
I won't get into all the spin-offs, but generally speaking, a lot of them are awesome. X and XV may be some of my favorite mainline FF games, but certain spin-offs are on my favorite games of all time list.