The DA-da-da-DUN chimes you get when you clear a stage, especially a difficult one (Ultimate Scores for Battle with the Four Fiends and Battle at the Big Bridge, anyone?).
The sound effect for when you pass the "Boss No. 02 or Boss No. 03" sign in the first half of a Dark Note, assuring you you're getting something good if you defeat the boss
The whirring noise made when a Dark Note's second half lets you know you're fighting the third boss, which has the best item drops.
BOOOOM! Yeah, you just defeated the boss. Let's see what it drops.
One for the developers: a high framerate is crucial to a Rhythm Game, so this game runs at 60 frames per second in full stereoscopic 3D.
Moogle Fans get one in Curtain Call, as in the VS section (Unless you find it annoying and disable it) Mog who is fully voiced will chime in during the battle telling you when whether you or your opponent passes to first place, or warns you when the battle gimmicks affects either player. Mog has been voicedbefore but here having a voiced Moogle being the battles' referee is pretty cool in itself.
There are two possibilities for the Ultimate Moment of Awesome for any player. Both are immensely satisfying:
Getting All Critical on an Ultimate Song the first time playing it (even more if the song was not previously played on lower difficulties).
Repeatedly failing to Perfect Chain a song and making several attempts and, not only getting the Perfect Chain, but an All/Total Critical of that same song on the successful attempt.
Another one for the player: When going for a certain bar on the Total Critical chart and getting that bar filled despite messing up on the bar both before and after it. Really makes the desired one stand out in the results screen.
The Extended Version of the Final Fantasy Medley when the music swells and the awesomeness of the entire series is summed up in the conclusion of that song.