I'll try to list at least one thing from each Final Fantasy.

Final Fantasy I: The four fiends, that require crawling through a gigantic superdungeon to get through.
Final Fantasy II: David Bowie as a primary antagonist.
Final Fantasy III: The Viking Class. Yarr-dee-harr-dee!
Final Fantasy IV: Defeating your Shadow self, Intriguing areas like the moon
Final Fantasy V: Gilgamesh and the Void
Final Fantasy VI: Something to look to when making a good story.
Final Fantasy VII: Something to stray away from if you don't want the community to be filled with blabbering anime fans.
Final Fantasy VIII: Something to STAY FAR AWAY FROM if you don't want the game to suck. Forever. DEAR GOD.
Final Fantasy IX: The way in which the game almost parodies the earlier final fantasy games.
Final Fantasy X: Meg Ryan with the voice and personality of Gilbert Godfreid. Also an example of how not to make a story.
Final Fantasy X-2: The bathing minigame. Because nothing's better than two lalafells rubbing and lathering each other down.
Final Fantasy XI: Please, no more. This game is XI enough.
Final Fantasy XII: The mark system, city and area design, cultures to take ideas from, interesting races.
Final Fantasy XIII: A city like nautilus. The Sunleth waterscape. Pretty much it.
Final Fantasy XIII-2: HOW TO FAIL AT CHARACTER DESIGN 101.