FF1 - Dungeon Hack and Slash
This game was mainly about killing things and exploring dungeons plain and simple.

FF3 - Class based Platformer
Because I had to work a platformer in somewhere, and this game had lots of 'theme' dungeons.

FF4 - RTS
Lots of big military battles in this one

FF5 - Puzzle based game
Combat based around solving puzzles with classes

FF6 - SRPG
Since you have such a big collection of characters, why not use them all in a strategy based game.

FF7 - Sandbox
Because GTA is so much cooler running around with a huge sword and sticking it to the ShinRa.

FF9 - Point and Click
Still lets you explore all the exiting locals while maintaining the charm of it's original incarnation.

FF10 - Oregon Trail
Make the pilgrimage to Zanarkand in old school style.
"Tidus has died of dysentery".

FF12 - Small squad based tactical game
Something like a medieval rainbow six.

FF13 - JRPG
....