This blog post is pretty old, but I'm currently playing Final Fantasy IV and stumbled across here.
 
#2 - Final Fantasy VII 
#4 - Final Fantasy VI
#7 - Final Fantasy V
#9 - Final Fantasy IV
 
Those are the ones I definitely know. I've never played V or VI, but V's clue gave it away, and I've seen videos of VI (I still intend to play the latter at some point).

#7 is FFV and #9 is FFIV.

Funny that the only one I recognized were the FF6 and FF7 battle themes.  Despite having played this series to death, I guess I never paid much attention to the music.

1) No idea 
 
2) FF7 
 
3) No Idea 
 
Boss Battle 1 - FF8
   
4) FF 5?
 
5) FF9 
 
6) No idea 
 
Boss Battle 2 - Final Jenova Fight 
 
7) FF6 
 
8) FF8 
 
9) No Idea 
 
Boss Battle 3 - No idea 
 
Final Battle - No idea

"Second one is the Jenova Battle from FF7. "

I'm pretty sure Boss Battle 1 is Kefka from FF6. But then again, that's the only game I've played.

Second one is the Jenova Battle from FF7.

Only having played 4 of the games mentioned makes this a bit tricky... but let's give it a go! (No prizes guessing which I've played.) 
 
1) FF3
 
2) FF7
 
3) FF1
 
Boss Battle 1) FF8
 
4) FF6
 
5) FF9
 
6)  FF2
 
Boss Battle 2) FF7
 
7)  FF4
 
8) FF8
 
9) FF5
 
Boss Battle 3) FF4
 
Final Battle)  FF5

Considering my foray into Final Fantasy VIII and my resulting re-obsession with the music of the series, I thought I'd put together one of my ol' music quizzes and test your mettle. This one's almost dumb-easy since it's the battle music, and the battle music is what you hear most, but I figured it'd be best to the Holidays off nice and easy.