Can be posted in any format. List, favorite of all time, favorite of the moment, that sort of thing.
Anyhow...at the moment, I feel particular fondness for the final boss music of Banjo-Kazooie, Diddy Kong Racing, and Mario & Luigi: PiT.
Thread's over, I win. 
Thread's over, I win.
No...
...you don't.
Not to mention boss battles like Hari-Hara (Digital Devil Saga), Dark Falz (Phantasy Star Online), Zowie (Gitaroo Man), Wizeman (NiGHTS: Into Dreams) and many more, you've far from won mah boi.
I'll admit, the second Vergil encounter music is pretty badass.
But seriously, I have yet to see any video game music out-epic the one-two punch of Ace Combat 4's final stage music.
For me, its One Winged Angel in Final Fantasy VII. Really epic.
Sonic 2 Eggsterminator Music. =D
S3&K- Doomsday Zone
The Nightmare Before Christmas: Oogie's Revenge - A Filthy Finale
God Hand - Devil May Sly (God Hand vs Devil Hand)
Note: Not QUITE the final boss music, but hey. It's close to the final boss and it's AWESOME.
No More Heroes - Vs Henry
Definitely Kirby 64's final fight with Zero-Two.
Thank you Cy. Henry's fight does have some awesome music. I was going to put that actually. As is Doomsday. And I agree with you too, TTG. I've got others, but I want to find them somewhereso I can post it.
"Favorite Final Boss Music"
It's in Megaman Legends... The Fight with, er... Teisel Bonne!? >>;;
The Sonic games come to mind
Sonic 1
Sonic 2
Sonic 3&K
Open Your Heart (Sonic Adventure 1)
Live and Learn (Sonic Adventure 2)
What I'm Made Of (YES THE GAME SUCKED BUT THAT SONG WAS AWESOME DAMN IT! =O )
Never Turn Back (Another awesome song with a horrid game. I know it was awful beyond comparison, but the song fits well)
Dark Falz (Phantasy Star Online)
This all I can think of now.
Well lets see...
Wrapped in Black- Sonic Rush
Ganon- LOZ:OOT
The final fight music in the first Devil May Cry
