Character Themes:

Hero: Celes' Theme (FF6) 22-Celes's Theme-FFVI OST - YouTube
Villain: Kefka's Theme (FF6) Final Fantasy 6 - Kefka Theme - YouTube
Field Theme: Crossing Those Hills (FF9) Final Fantasy IX OST - Crossing Those Hills ~ World Map Theme #1 - YouTube
Airship: The Airship (FF4) http://www.youtube.com/watch?v=bf5fp7MNUiA


Battle Themes:

Normal Battle: Tie between Battle 1 (FF5) Final Fantasy V OST - Battle 1 ~ Battle Theme - YouTube ,and Battle 1 (FF9) Final Fantasy IX OST - Battle 1 ~ Battle Theme - YouTube
Boss Battle: Boss Battle (FF4) Final Fantasy IV OST : 13 - Boss Battle - YouTube
Special Boss: Dark Messenger (FF9) Final Fantasy IX OST - The Dark Messenger ~ Battle against Trance Kuja - YouTube
Final Boss: Dancing Mad (FF6) Classic VGM 278: Final Fantasy VI - Dancing Mad (Full Song) - YouTube

Other Themes:

Chocobo Theme: Chocobo Chocobo (FF4) Final Fantasy IV OST - Chocobo Chocobo ~ Chocobo Theme - YouTube
Town Theme: Welcome to our Town! (FF4) Final Fantasy IV OST - Welcome to Our Town! ~ Town Theme - YouTube
Dungeon Theme: Tower of Zot (FF4) Final Fantasy IV OST - Tower of Zot - YouTube