Too many. I know them by melody rather than name for some of them, such as what I can only assume is Serah's theme (lala lala la la, lala lala la, lala lala la la la )? Anyway, of those that I actually know the name of, I'd say these have stuck with me most...

Liberi Fatali
One Winged Angel
Aerith's Theme
Turk's Theme
Shinra Company
Those Who Fight
Still More Fighting
Fanfare
Various versions of the Chocobo Theme
Main Theme (VII)
Snow's Theme
Answers

So basically Final Fantasy VII's soundtrack and a few others, I guess.