Regardless of placement, all video game music needs to match the circumstance. Sometimes this is even more important than being a good listenable piece. Consider what happens when you're fighting Giygas in Earthbound for example; you know, what happens after Pokey turns off the Devil's Machine. The utter discord of the background noise sounds simply terrible but that's what sets the mood. It's a virtually hopeless, confused mess of static and sorrow that you don't even want to listen to. It conveys the creepy madness that is Giygas, the utterly dreadful fear in the otherwise optimally cheerful protagonist's hearts and rounds out the game's utter weirdness by bringing a grim dark serious tonality to the game which would've otherwise been absent. As music, it sucks but as part of the atmosphere it's utterly irreplaceable in function. It's just a shame that the protagonists couldn't experience it in the flesh for it to make their skin crawl. It really diminishes almost every aspect of the conflict to swap out their bodies. The whole drama angle wouldn't have needed much reworking at all.
Of course the game would've been just as good if the climatic battle was set to Yakety Sax, assuming the context was reworked to be more comedic. Yakety Sax is often used for the main conflict in a comedy of errors, of the sort Earthbound kinda built itself up to be. It just couldn't have been anything more "traditional" like Poky Means Business, because as great as that theme is, it doesn't bring the situation over the top enough.
On an entirely unrelated note, I wanna hear The Flight of the Bumblebee used someday.
Depends entirely on the game, and the fight. Some final boss fights are hopeful struggles for the fate of humanity, others are crushing doom in your face.
A few really good ones:
The Almighty (http://www.youtube.com/watch?v=FGUGAHTPcak) from Persona 4 - Yes, I know Ameno-Sagiri isn't the TRUE final boss, but it is for the normal ending, and The Almighty gives all the vibes associated with P4 as a whole and this fight in particular, in addition to being a particularly wonderful piece of music.
The Day The World Falls (http://www.youtube.com/watch?v=UEm_ssPFGD8) from Luminous Arc 2 - This is interesting, because it's an SRPG, so it's the theme for everyone on the field at the same time (I'm using LA2 as a stand-in for the genre, or I'd include a bunch more). It mixes the right amounts of fear, despair, tension, and that one quiet section of just the harp and violin together that speaks of the hopes that ride upon this last, desperate fight. Once again, Yoko Shimomura is a bloody genius.
The Final Battle (http://www.youtube.com/watch?v=qFdHWhLpHbw) from Riviera: The Promised Land - I add this one because it's a good example of a final battle that sticks to predominantly major keys; as such, it comes off much heavier on the "hope" side and less on the "fear". However, it still contains the energy and power expected of a final boss, and it works.
...a good example where this doesn't: Emotional Skyscraper ~ Cosmic Mind. ZUN's final boss themes are exceptionally varied for the work of one man, usually consisting of several discrete parts. Moving into major keys is by no means a bad thing: it can be done, and done well. History of the Moon is major as all hell, and it's pretty sweet. However, Cosmic Mind simply lacks the energy, the pacing, the punch of a final boss theme. It is eminently fitting for Byakuren's character, but it doesn't make for a fitting final boss.
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