I'm a loyal fan through and through, but I gotta say, I haven't got much hope for the series these days. My opinion of XIII gets worse every time I hear about it, and Squareenix's "10 years 'til the true sequel, have 780 crappy ports while you wait lololololol" has not filled me with a great deal of confidence.
That said, these are my favorite entries in the series.
II(IV), SNES - It was my first Final Fantasy, and despite the fact that I didn't actually beat it until the more faithful PSX port years later, it's very dear to me for it's compelling storyline and fun dialogue.
VI, SNES - What really impresses me about this game is the fact that the cast is huge, yet each one manages to bring a compelling story to the table. I don't think I've played a game since about which I could discuss the character's backstories, personality traits, emotional baggage and eventual redemption.
VII - Say what you will about the rabid fanbase, I enjoyed VII for what it was; an excellent RPG with an interesting skill system and a story that might be a bit ludicrous at times, but still manages to be entertaining.
Tactics - Oh man, this one had it all. The winding, intricate story, the compelling characters, the gameplay, the secrets, the replay factor... For me, it is the ultimate Final Fantasy game, and it's a shame that it doesn't get the recognition it's due.