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I'm pretty sure this list now includes every FF game ever made, if you know of any that I haven't included, say so in the comments.

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Normal = Owned, unfinished
Italic = Damaged / need to (re)purchase
Underlined = Currently playing
Bold = Finished

I wish there was a strikethrough font :(

Final Fantasy
Final Fantasy II
Final Fantasy III
Final Fantasy IV
Final Fantasy IV: Interlude
Final Fantasy IV: The After Years
Final Fantasy V
Final Fantasy VI
Final Fantasy VII: Before Crisis
Final Fantasy VII: Crisis Core
Final Fantasy VII
Final Fantasy VII: Dirge of Cerberus
Final Fantasy VIII
Final Fantasy IX
Final Fantasy X
Final Fantasy X-2
Final Fantasy XII
Final Fantasy XII: Revenant Wings
Final Fantasy XIII
Final Fantasy XIII-2

Final Fantasy Legend
Final Fantasy Legend II
Final Fantasy Legend III
Final Fantasy Adventure
Final Fantasy: Mystic Quest

Final Fantasy Tactics: War of the Lions
Final Fantasy Tactics Advance
Final Fantasy Tactics A2
Final Fantasy: The Four Heroes of Light
Dissidia 012 Final Fantasy
Final Fantasy Type - 0
Theatrhythm Final Fantasy
Final Fantasy Dimensions

Final Fantasy Crystal Chronicles
Final Fantasy CC: Ring of Fates
Final Fantasy CC: Echoes of Time
Final Fantasy CC: The Crystal Bearers

Chocobo's Dungeon
Chocobo's Dungeon 2
Chocobo Racing
Chocobo World
Final Fantasy Fables: Chocobo Tales
Final Fantasy Fables: Chocobo's Dungeon
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Final Fantasy: The Spirits Within
Final Fantasy VII Advent Children
Final Fantasy VII Advent Children Complete
Final Fantasy VII Last Order
Final Fantasy: Legend of the Crystals
Final Fantasy: Unlimited