1. Tifa - I like the contrast between her tough fighting style, sexy attire and gentle/caring personality. I like that rather than being the damsel in distress, she was the hero that saved the hero in distress. Being in my all time favourite game helps, naturally, but she overtook Red XIII as my favourite character after my second or third playthrough.
2. Snow - I really didn't like this guy but oh god did he grow on me more and more. I like confidence and encouragement, and he has these in spades, even if he is a complete idiot most of the time (which is also endearing to some extent).
3. Gilgamesh - This guy is amazing and I love it every time he features in a game. His contributions to FFV, FFXII and FFXIV in particular were a joy for me.
4. Red XIII - I loved this guy when we first met him. I loved him all the way through to him arriving at Cosmo Canyon. I hated how he suddenly went from this wise creature who has lived many years more than others in the gang to this baby who acts like he needs a cuddle all the time. The personality change in him was bigger than the personality change in Cloud, and that's saying something. Still, he gets a place for being a badass looking creature and for how he was up until he regressed.
5. Lulu - I liked her about as much as the other non-lead party members in FFX, but it was the webcomic by DippyWerewolf that covers her history before the events of FFX that really made her a favourite of mine, even if I haven't played the game again since.
6. Cloud - I love everything about his story. Let's just forget how troutty he sounded in Crisis Core and how emo he was in AC and just enjoy FFVII itself, and his cameo in WoFF too. Love Cloud when he's confident and has a bit of attitude.
7. Tiamat - From Final Fantasy XIV. An NPC dragon with very little involvement but I love her story, what she has been through, and how it has moulded who she is today. I hope someday we see her free and happy. I get really interested every time I stumble into a cutscene that she features in, because I'm just fascinated by her.
8. Jonny - The series needs more characters like this. Just a dude going about his business and traveling the world while occasionally catching up with his friends who happened to go on to become the saviours of the world. <3 Jonny xD
9. Raubahn - Too many spoilers to go through so I'll just say I love this guy for all he has brought to FFXIV as a leader. Probably my favourite official (ie governing in any way) leader in the series.
10. Zack - Tough to edge out the others below, but I adored him in Crisis Core.

Special Mentions
Sephiroth - Best villain.
Yshtola - My fave of the Scions in FFXIV, who are the prominent NPCs.
Hildebrand - Not so much the character but his entire plot in Final Fantasy XIV is excellent slapstick fun.
Hraesvelgr, Nidhogg, Bahamut, Midgardsormr - These four dragons all are fantastic in FFXIV. The sheer brute power of the summoned Bahamut helped make End of an Era become my favourite cutscene in the history of Final Fantasy. Hraesvelgr and Nidhogg are excellent characters but I can't mention one without the other, because their story is what truly makes them. Midgardsormr loops in with all the FFXIV dragons (including of course Tiamat who made my list) excellently.
Fujin/Raijin - Arguably best duo. Hilarious.
Wedge/Biggs (FFVIII) - Arguably best duo. Hilarious.

Cheat Mention: Loony Bob - My character in FFXIV.

Probably missing a bunch that have eluded me though.