Several themes are known and loved throughout the series. Some have stayed more or less the same; others have been completely redone. I don't have every single MIDI, but I have enough to get an idea of what the music of this series has gone through.

Prelude
Prelude, the first song ever heard from Final Fantasy, has remained relatively unchanged throughout the series. FF4 added a flute melody to the original arpeggio. This did not change until FF10 altered the song into a funky disco beat.

FF: Prelude

Chocobo Theme

The original theme, from FF2, only contained half of what I consider the "base" theme.

FF2: Chocobo!
FF3: Chocobos!
FF4: Chocobo-Chocobo (yellow), Samba de Chocobo (black)
FF5: Go-Go Boco! (yellow), Mamba de Chocobo (black)
FF6: Techno de Chocobo
FF7: Waltz de Chocobo (Chocobo dancing!), Electric de Chocobo (battling Chocobos!), Cinco de Chocobo (riding Chocobos), Fiddle de Chocobo (racing Chocobos!)
FF8: ODEKA ke Chocobo (Chicobo theme), Modes de Chocobo (riding theme)
FF9: Aloha de Chocobo, Ukelele de Chocobo (riding Chocobos)
FF10: Chocobo Jam [Brass de Chocobo]

Victory Fanfare

FF1: Victory Fanfare
FF2: Victory Fanfare
FF3: Fanfare
FF4: Fanfare
FF5: Victory's Fanfare
FF6: Fanfare
FF7: Fanfare
FF8: The Winner
FF9: Fanfare
FF10: Victory Fanfare

Main/Overworld Themes

FF1: Main Theme
FF2: Main Theme
FF3: Eternal Wind
FF4: Main Theme
FF5: Four Valiant Hearts
FF6: Terra, Searching For Friends
FF7: FFVII Main Theme
FF8: Blue Fields
FF9: Over The Hill
FF10: N/A
FFMQ: World
FF Tactics: World Map

Battle Themes

FF1: Battle Scene
FF2: Battle 1
FF3: Battle 1
FF4: Fight 1
FF5: The Battle
FF6: Battle Theme
FF7: Fighting
FF8: Don't Be Afraid, The Man With The Machine Gun
FF9: Battle 1
FF10: Battle Theme
FFMQ: Battle 1

Boss Battle Themes

FF2: Battle 2
FF3: Battle 2
FF4: Fight 2, The Dreadful Fight
FF5: The Fierce Battle, The Decisive Battle
FF6: The Decisive Battle, The Fierce Battle
FF7: Still More Fighting
FF8: Force Your Way
FF9: Battle 2
FF10: Enemy Assault
FFMQ: Battle 2

Airship Themes

FF1: Airship
FF2: The Airship (unreleased track)
FF3: Go Above The Clouds!, The Invincible
FF4: The Airship
FF5: The Airship
FF6: Blackjack
FF7: The Highwind Takes To The Skies!
FF8: Ride On
FF9: Airship ~ Hilda Garde
FF10: Launch

Final Boss Themes

FF3: This Is The Last Battle
FF4: The Final Battle
FF5: The Last Battle
FF6: Dancing Mad Part 1, Part 2
FF7: One Winged Angel
FF8: The Extreme
FF9: The Final Battle
FF10: Final Battle
FFMQ: Battle 3