Quote Originally Posted by aisle_s
Well the logos generally have something to do with the game.

IV: Cain is the logo
V: Reina's Hiryuu is the logo
VI: Terra riding the Magic Armor is the logo
VII: Meteor is the logo
VIII: Squall+Rinoa are the logo
IX: The Crystal is the logo
X: Yuna is the logo
XII: A judge is the logo
XIII: ?

I think we can safely assume these characters will have something to do with the storyline.
Also, II had the Emperor as its logo, X-2's logo was Yuna, Rikku, and Paine, and III had Dark Cloud as its logo.