Because the list of songs actually being played is massive, here are the games I have songs for that are playing. They may or may not include the complete soundtrack.

Arc the Lad
Arc the Lad II
Arc the Lad III
Arcana
Breath of Fire
Breath of Fire II
Breath of Fire III
Breath of Fire IV
Chrono Cross
Chrono Trigger
Crystalis
Der Langrisser
Dragon Quest
Dragon Quest II
Dragon Quest III
Dragon Quest IV
Earthbound
Final Fantasy
Final Fantasy Black Mages
Final Fantasy II
Final Fantasy III
Final Fantasy IV
Final Fantasy IX
Final Fantasy Legend
Final Fantasy Legend II
Final Fantasy Tactics
Final Fantasy V
Final Fantasy VI
Final Fantasy VII
Final Fantasy VIII
Final Fantasy X
Genso Suikoden
Genso Suikoden II
Great Greed
Langrisser
Langrisser II
Legend of Mana
Lufia
Lufia II
Lunar - Silver Story
Phantasy Star Online
Phantasy Star
Phantasy Star II
Phantasy Star III
Phantasy Star IV
Romancing Saga
Romancing Saga II
Romancing Saga III
Saga Frontier
Secret of Evermore
Secret of Mana
Seiken Densetsu
Seiken Densetsu II
Seiken Densetsu III
Shining Force
Shining Force II
Shining Force III
Star Ocean
Star Ocean II
Startropics
Suikogaiden
Suikogaiden II
Terranigma
Xenogears
The Legend of Zelda
Zelda - A Link to the Past
Zelda - The Ocarina of Time
Zelda - The Wind Waker
Zelda II