Mega Man Battle Network games's final boss themes never had chanting, and KH Days has Vector to the Heavens and/or Another Side.
Alt account of Angeldog 2437.
Lizard Metabolism
Komato General Tor appeared. He's saddened by the fact nobody mentioned his theme yet.
https://www.youtube.com/watch?v=86IxmklUgEM&feature=related
Mega Man in general had awesome chanting-free final boss themes. I'm particularly fond of "Vs. Nebula Grey" from Mega Man Battle Network 5:
![[up]](https://static.tvtropes.org/pmwiki/pub/smiles/arrow_up.png "[up]"){kind=icon}
The DS version of that theme is cool too. 
slice of lice
I was about to list more Guilty Gear/Blazblue themes, but one good one was already posted and most of them have chanting.
Midnight Carnival is pretty crazy though. Even with a slight choir-ish backing. [[youtube:watch?v=LKJ9AVrpM9s]]
Another one, Kill DOG as a sacrifice to DOG eschews chanting for RRHRHARHAHRUHARUHRAURHAHURG.
https://www.youtube.com/watch?v=RZmwRmVSS6c
edited 16th Oct '11 3:04:40 PM by OuthouseInferno
Forget the tropes until after you're done.
Face Time
Sick and tired of all these silly orchestral and latin chanting Jecht decided he wanted a heavy metal theme for his battle. So he did.
Avvie-free for life!
I think it must be noted that developers who can't afford to hire a chorus and related professionals in addition to a band or orchestra can't have chanting in their final boss theme. Games from systems that can't handle vocals very well will also lack chanting.
An interesting note about ZUN: he uses some synth tricks to mimic chanting in certain boss themes. Kanako's in particular.
That's a lot of final boss themes without chanting. I think the majority of games lack chanting in their final boss themes.
edited 17th Oct '11 12:05:59 AM by Recon5
slice of lice
Synth chanting has been accessible to anyone with 16-bit instrument capabilities and on. Dancing Mad from FFVI is the most prominent example to me.
It's not a "trick" that ZUN uses in Suwa Foughten Field, it's an actual MIDI chant intstrument.
edited 17th Oct '11 12:29:18 AM by OuthouseInferno
Forget the tropes until after you're done.
...unless you consider "1 2 3! 1 2 3! OK Don't Mind! Hey You Can Do!" chanting... and I'm sure it counts as a final boss.
Also, Pokemon Champion music.
Also, because any thread about video game music cannot have enough Touhou examples, Flight of the Bamboo Cutter ~ Lunatic Princess and Shoutoku Legend ~ True Administrator.
edited 17th Oct '11 12:27:25 AM by stardf29
Bad game good tune.
Let the sun shine upon you and grace you with it's divinity.
edited 17th Oct '11 12:34:47 AM by Envyus
I like this one it's more recent than most examples here and it has a real panic-y tension to it:
edited 17th Oct '11 12:52:55 AM by AnOtherT
Oboro Muramasa had a wonderful soundtrack. This track never fails to inspire terror...
Alternatively, there's always the other final boss...
...
Parasol Star Memories
Fergard, you may want to double check.
So. Let's all pause for a moment to smell what the Rock was, is, and forever will be... cooking.—Cave Johnson
Nerds nearly need needy nerdy nerds
Kagome, Kagome
Here are two good themes from the Megaman series