My favorite boss from any videogame is a tie between Ganondorf/Ganon from Ocarina of Time and Bowser from Super Mario 3D Land. Both battles actually draw several distinct parallels. After defeating Ganondorf and escaping from his crumbling castle, there is a moment of silence as the battle seems to have ended and the wind blows peacefully. The same effect is used after sending Bowser into the abyss below for the first time in the final World 8 Castle. Also, after these moments the two bosses return reinvigorated and stronger than ever before. Personally, these are the pinnacle of gaming boss battles and a model for other developers on how they should be handled.
Phalanx, the thirteenth colossus from Shadow of Colossus, was the best I've ever played through. It goes along with a huge theme of the game where you feel guilty for having to kill the innocent monsters. It never caused you any harm... Just the atmosphere alone, my god.
Other favorites include Xemnas and his many many phases from Kingdom Hearts II, the classic Metal Gear Rex fight from MGS1, any of the bosses from M&L Superstar Saga, and the overkill that was Jubileus from Bayonetta.
Man this is tough. Reeeaaaal tough. Okay so here goes my favorites since I can't specify a single one.
Quadraxis from Metroid Prime 2. The take down, like each big boss in a Metroid Prime game, was multistaged and quite challenging. Compound that with the fact that due to the atmosphere of Dark Aether you're constantly taking damage and there are no safe zones to keep the damage off you. Plus Quadraxis is 50 ft. tall four legged robot so that's cool.
Dark Samus from Metroid Prime 3 was also really good. It provided that final boss type fight with a really good combat basis.
The Ridley fight in Metroid Other M. The death blow had Samus shoot a laser down Ridley's throat. That's awesome.
As a foot note there are tons more I love but these make some of the best.
Mine is Ganondorf from the wind Waker. The whole set up is great. The hopelessness Ganondorf is facing and he turns around and laughs! Then he goes to mock the triforce what he has been trying to get for years! The final blow to the forehead was epic way to get rid of him.
i always liked the optional demon wall fight in FF12. even if you leveled up alot before fighting it, not being able to slow it down and the shorter area it moves in makes it even better than the one you do to progress.
apacrypha the final boss of radiant historia they did everything right with this boss and it did not come out of no were
heiss summons it so the he and stoke can hear the emotions of the past sacrifices
The music fits so perfectly it feels like the end of the world is near and you can lose you have to win. Not to mention the scene you get for the true ending it is truly sad which is the way the story ends. They combined all the right elements to convey the almost perfect final boss.
for me gotta go with Bowser in Mario 64 that music was just scary and epic as a little kid, Ganon from OOT, Dracula from Castlevania, Ultimicia from FF8, Dark Genie from Dark Cloud, Night Terror from SC3, and by far one of the most epic battles of all time Kefka from FF6