There's also the Final Fantasy IX song Grand Cross. While not being sung by Necron himself and not having lyrics at all, this is still a music that contains lot of people screaming in panic and agony, which kinda goes along with Necron, being the embodiment of humans' fear, helplessness, and suffering when faced with death.
Arguably, again from Jonathan Coulton and again in a VALVE game — one of the songs that plays on the jukeboxes scattered around Left 4 Dead 2 is "Re: Your Brains", a song about an office worker turned zombie telling his still-human surviving coworker what he and his flesh-eating companions will do when they get to him. Bonus: When the chorus starts up, an in-game Horde attacks. And they snarl in-tune to it.
Conker's Bad Fur Day has "Sloprano", an opera sung by the Great Mighty Poo, a giant singing pile of feces. The song is actually key to defeating him, as he sings higher and higher notes as you attack him, until finally he sings a note pitched high enough to shatter the glass blocking the toilet cord.
Marjoly and crew also have such songs in the game's two sequels, and in the 2nd game the villain Akujo has a similar tune.
"Kuttetekaruna", from LocoRoco, has no "real" lyrics to speak of... but it's hard to call it anything other than a villain song, given the frightened voices of its singers and its use of maniac laughter.
There's also "Merure Merure", the Nightmare Before Christmas-esque song that plays while you're exploring the innards of the final boss.
The spinoff game "Midnight Carnival" has a catchy jazz number sung by the BuiBuis, who collectively served as Dragons to the villains in the last game and now act as the main villains. They also sing their own arranged versions of songs from the previous games during the levels, including the aforementioned "Kuttetekaruna".
The War Song from Abe Lincoln Must Die! may just qualify, as while the character isn't particularly villainous, his desires certainly are, as revealed by his love of bombs and guns (And so much more!) and his unbridled joy that a war has begun.
Sam & Max Beyond Time And Space: T-H-E-M gets a big mariachi musical number in Chariots of the Dogs explaining why they steal souls in a time-traveling flying saucer.
The educational computer game I. M. Meen opens with a catchy Villain Song from the titular villain about his plan to trap studious little bookworms in a magic labyrinth using a magic book. It almost makes up for the fact that it and all other cutscenes were animated by the same people who animated the dreaded The Legend Of Zelda C Di Games (though that has lead to Meen becoming popular in several YouTube Poop videos).
For Sonic Adventure 2, the theme for Biolizard boss battle, Supporting Me:
"I believe in my future, farewell to the shadow. It was my place to live, but I need your hand. Lead me out with your light, I've breathed in the disgusting air of darkness, but I never lose out."
Though not exactly evil, Team Dark's (Shadow, Rouge, and E-123-Omega) theme This Machine is arguably the best theme among the 4 teams' theme songs, and it's about the three members of the team who were marked as villains in the previous game, or built by the villain in Omega's case.
They also brought back Throw It All Away and All Hail Shadow. Also, Shadow's page on the Sonic wiki has a whole section of theme songs related to him, and it even makes of note of saying that the lyrics are hard to understand in most of them. Oh, and for a mind boggler, remember Live and Learn? Yeah, the main theme and final boss music of Sonic Adventure 2? They actually attribute that as his theme.
Which actually makes sense, considering that the song is about letting go of the pain in one's past.
Metal Sonic has many themes (Yes really!), which fit him extremely well:
From the Genesis era, "Metal Sonic" from the Sega Virtual Tunes, about his purpose and personality.
From Mystical Ninja Starring Goemon, we have Spring Breeze Dancin' and Kitty Lily's secret weapon: Gorgeus My Stage. An awesome Broadway-styled musical act that, without a doubt, will turn anyone into a Peach Montain Shogun "hard-die fan". Or so they claim.
And in the sequel, we have Philistine, sung by Margaret. The Japanese version has its own remix. The song is largely Margaret mocking Travis for being a "fucking Philistine" with a petty and childish idea of being a "hero" and a badass while he's in reality a loser otaku.
"Look Pimpin'" from MadWorld is a hip-hop Villain Song by Sick YG, sung from the perspective of the Final Boss, the Black Baron, during the game's climactic battle. Once half the boss's health is gone, the music switches to "So Cold" by Ox, which is still a villain song; however, while "Look Pimpin'" mocks Jack for thinking he can defeat the Black Baron, "So Cold" is him enraged by how he's gotten beaten up.
The other boss themes are also villain songs, though not as focused. "You Don't Know Me" by Bandy Leggz (the female boss music) in particular is girl power gone mad.
"Nightfall" from World of Warcraft's own rock band Level 80 Elite Tauren Chieftain starts out as a villain song sung by a death knight of the Ebon Blade, before the end describes the Knights being betrayed and swearing vengeance upon the Lich King.
"Ignorance Is Bliss", by Jellyfish, is sung by Bowser to Peach. It came out on the album "White Knuckle Scorin'", which had a comic story insert based on Super Mario World. (Although the comic had the characters continually referencing the titles of the songs on the album, this song was the only Mario-themed song on the album). The song and comic is about Bowser wanting to turn Dinosaurland "into nothing than fossil fuel" and join OPEC but his arrogance doesn't let him admit that not knowing how to read is the problem.
Don't forget Aribeth's theme (from Neverwinter Nights) when she does a complete face-heel turn. Their "evil theme" is played when the Player character encounters them near the end of the game and can also be found in the game's toolset.
Ape Escape 3 has "Banana Heartbreak"; it's not so much a Villain Song as a song by a villain for most of it, but in the last verse it turns twisted by Ape Escape standards.
Agreed. Nothing says "theatre" like multiple-personality barbie-esque monkeys in pink dresses. Just sit back and listen to banana heartbreak/I WILL CRUSH YOU.
In Disney Universe, the main villain, Hex, tortures us at the end with a rock remix of "It's a Small World", and while doing so, the enemies are seen torturing themselves through various antics.
When a song from the Shin Megami Tensei series is used, it's usually in the Persona series and about how awesome the heroes are or cheering them on to their goal, maybe something a bit deeper. Shin Megami Tensei III: Nocturne seems to be an exception. The Fierce Battle theme seems to be the angels singing to you in hatred for how you've abused your power to go against them, while the main Boss Battle theme is the demons singing about why God despises them, with a bit of the desperate remains of humanity (and possibly a few demons) begging for salvation. Each of these sides can be villains to you in the end.
An interesting example is "That's Amore" of Psychopath Bibi Love from Dead Rising 2. At first listen, it really doesn't sound much more than what you'd expect of a love song. But consider it has lyrics like "You better do what I say!/Say you love me today!" when she's threatened to blow up several innocents unless you help her performance.
Anarchy Reigns has a few of these around. Baron's new track doesn't fit since he's fighting with the good guys here, but there are two better examples. First there's Max's theme Unlimited Resources, which is basically Max singing to you about how he is just going to wreck your shit. The other song is the final boss track against Nikolai called Find You. The song takes place from the villain's perspective completely and how his view of the world has become dark and hopeless, telling Jack and Leo that their only option is to find the truth before the truth finds them.
In Nazi Zombies, "Not Ready to Die" definitely seems to be Dr. Richtofen's villain song, while "115" seems to be Samantha's.
The boss themes from Metal Gear Rising: Revengeance all start out as instrumentals, then gain lyrics and become Villain Songs once the final phase of their boss fight starts.
"The Only Thing I Know for Real" for Jetstream Sam, about how the only thing he knows is fighting and killing others, and how he doesn't even know his own reasons or motivations for doing so (and never gets to find out before Raiden kills him).
Scooby-Doo! Night of 100 Frights features four Villain Songs for each of the four bosses: the Black Knight, the Green Ghost, the Ghost of Redbeard, and the Big Bad, Mastermind. For the first three, it's just a background choir during the fight, but Mastermind has a few lines in his song.
The remake of Lunar: The Silver Star has the song of Dark Althena/Luna. No actual lyrics aside from her going "ahhhh ahhhhhh, ahhhh ahhhhhh ahhhhhh ahhhh ahhhhhhhhhhhhhh," but still pretty memorable nonetheless.
"Noodles Can't Be Beat" from Parappa The Rapper 2 is a Boastful Rap by Colonel Noodle about how noodles are superior to other foods, with Parappa countering by listing a bunch of other non-noodle foods. During the final portion, it turns into more of a Heel Realization song as Colonel Noodle realizes how close-minded he's become.
In Crypt Of The Necrodancer: Amplified, Fortissimole gets a Boastful Rap, Notorious D.I.G., for his boss music, in which he mocks the player for thinking they can possibly defeat him. When Fortissimole is finally defeated, the background music continues, but his rap is cut short.
My manner is bombastic, my statement's sarcastic, My flow's pyroclastic, my legend's dynastic, Yeah, when I rise like Lazarus, my odor is always hazardous, Your skill is, at best, average, there's no way you can handle this!
Cuphead has Die House, which is sung by King Dice, The Dragon to the Devil, threatening Cuphead and Mugman and reminding them who's boss. It features many Creepy Jazz Music elements, such as a call-and-response segment, that bring to mind some of the haunting tunes by Cab Calloway, who was a big influence on the game's soundtrack. And all of this when he's just acting as an NPC Roadblock.