I have to agree with Prime_2 that the "Border of Life" remix is probably the best I've heard.
Someone listed Okami, and I have to post this... I know it isn't a boss music, but it precedes some of the most notable bosses in the game. The whole tone of the game was foreign to me, but I grew to love it, and the music definately was instrumental in winning me over.
Okami: Kushi's Ride
The Sonic 3K final boss theme is definitely a terrific theme as has been noted by many of the other members. Although I have to say that props have to be given to the Sunset Park train theme...
Sunset Park 3
And... lets not forget Robotnik's theme from S2...
And this does it justice
The fact that the main theme of Unleashed was
not the lyrical theme was instrumental in making its final boss music truly exhilarating.
Perfect Dark Gaia
And who can forget
Running Hell... just when I thought nothing could beat the
Final Cave.
Naturally, the music in Super Mario Galaxy
must be mentioned even if the boss itself was somewhat easy for a final boss.
The first time I played it, I was able to enjoy Sonic Heroes for what it was, although now I couldn't bear the slippery controls. I still can't deny that it had some
pretty decent music accompanying the final boss.
So those are probably my favorite boss themes or themes associated with bosses. Although there are some others that deserve honorable mention:
Theme of Kaiser
Vectorman 2 Lava Boss and Spider Boss
Vectorman 2 Shadow Nose