The only games prior to FFXII that actually "open" with that song are FFI, FFIII, and FFIV. But it's still present in the rest of the games mentioned.

This is, of course, if you're talking about Prologue. If you're talking about Prelude, that's been in FFI through FFX, although FFVIII only features a few notes from it during its ending credits and Game Over screen, and FFX was cursed with a crappy electronic remix version.