Related: Wild Man Fisher (a Dr. Demento staple) had "I'm The Meanie," about the villainous creatures from Yellow Submarine.
'The Watchmaker's Apprentice' by the Clockwork Quartet is from the POV of a disgruntled ex-employee framing his boss for murder. As the song progresses, he gradually gets more and more unhinged.
I rigged up a watch to do more than just chime,
And I didn't balk once at the depth of my crime!
The most perfect invention, that still kept impeccable time!
"Mack the Knife". adapted from the German Dreigroschenoper. Who knew so many wholesome 1950s singers could get away with singing gleefully about a spree killer and thief? (Not to mention that in the 1980s McDonald's famously adapted it - and some would say briefly covered it up - as "Mac Tonite.")
In Tom Smith's concept album The Last Hero on Earth there's both "Mad Scientists United" and "The Sinister Cavortings of Sir Wilfred P. Hufflebaggins III" (There's a reason why of him you never have heard).
"When You're Evil" fits this rather well while being generic enough to work for most any villain. Here's a video made using various Disney villains. See the Cartoons sections below for his other works.
A few others are "BRAINS!", "Almost Human" (a villain song for Lucifer, no less), "Ex Lover's Lover" and "Dead Girls".
The Electric Prunes' "Dr. Do-Good" from their second album Underground, while featuring the titular hero in the chorus, is mostly the insane ramblings of a villain, possibly the Dastardly Whiplash type.
Electric Six's "Naked Pictures (of Your Mother)" is about a government man using blackmail to get sex, "We Were Witchy Witchy White Women" is sung by evil witches, and Dick Valentine's side project Evil Cowards have "Love Pigs" and "Fixing Machines". "Watching Evil Empires Fall Apart" and "Steal Your Bones" are both subversions about Anti-Villains.
Janeen Brady's Standing Tall series - 12 tapes highlighting 12 virtues - includes the tape Gratitude, in which the most enjoyable song is the Rabbit's Villain Song close to the beginning. Of course, the song itself is Anvilicious, and the guy learns his lesson by the end and pulls a HeelFace Turn, but hey:
I never say thank you, I never intend Nobody likes me - but who needs a friend? I never say thank you, don't even know how And it's too late to change that now!
"Mordred's Lullaby" is about Morgause singing a prophecy to her son about how he is going to be used to bring about King Arthur's destruction — and die in the process.
The song "Medusa" may also be qualified as this. It is mostly about being yourself in the face of others, through the Point of View of Medusa.
"My garden's full of pretty men who couldn't stay away."
"Joan" can qualify depending on how you look at it. "I kill without consequence", after all.
"Crashing Down" is officially about Mordred convincing his men to rebel against King Arthur.
Golgotha is a borderline example, since it's about someone in a dystopian world who thinks it isn't their place to do anything.
Iron Savior has a few songs exemplifying this, notably "Protect the Law", by the titular starship, and "Protector", about the now-quite-deranged creator of said titular starship. "Outcast in the void, now I'm stronger than before / Landed to retake the crown, your conqueror comes ashore!" The villain gets the best lines indeed.
Ra's song Parole, is about the P.O.V. character leaving prison to pursue what is presumably an ex who is the reason he was put away to begin with. The lines include, "I called your mom and she told me/That you're afraid of me," and "I won't be disregarded/I won't be turned away/We'll finish up what you started/You're gonna pay today."
The kraken is evil? He's more sympathetic, like the vampire in "Blue Sunny Day". "Skullcrusher Mountain" is really a Villain Love Song... but the other ones, definitely. Also, don't forget "I'm a Mason Now" - while not inherently villainous, it's certainly vengeful and gloating.
The villainy of the kid from "The Future Soon" is also debatable - he announces his intentions to end world hunger, but then soon starts talking about how his robots are probably going to start a war on Earth and he'll end up kidnapping the girl he has a crush on when she rejects him. It's possible that the latter parts are just the painful reality that he'll always be a loser intruding on his otherwise nice fantasy.
"Live" by Paul and Storm is all about a mad scientist's desire to create an undead bride. Though it's arguably the villagers who are more villainous as they burst in and kill him as he and his bride finally get to be together. It's worth noting that Paul and Storm wrote this song as a parody of Jonathan Coulton's songs in the same vein. His response was to write a song parodying their music, called "Big Dick Farts a Polka".
Considering Lordi's stage act, this is pretty much par for the course for them — a band of monsters, singing about the things that make them monstrous. Examples can be readily found on every album of theirs so far.
Ayreon's The Human Equation has Day 16: Loser, which is basically the protagonist imagining his father (named Father, for simplicity's sake) showing up to gloat about how much of a failure the protagonist is, throwing various insults at him and claiming that even though he's constantly sued by his exes and half his kids are in jail, he still always comes out on top. It doesn't fit the formula perfectly, but it certainly gets the over the top gloating tone perfectly.
Doctor Steel is the embodiment of this trope. Almost every song he produces is from the viewpoint of Well-Intentioned ExtremistMad Scientist Dr. Steel. Particularly "Back and Forth" which is designed as hypnotic propaganda, and "Ode to Revenge" in which he laments the state of society, and calls up his legion of followers (Toy Soldiers) to "burn it all down".
Alice Cooper's songs are kind of like this, especially "Black Widow" and "Devil's Food".
Of particular note is "Nothing's Free" which serves as the villain song for The Showman of his concept album "The Last Temptation" and the Neil Gaiman penned comic of the same name.
The metal band Sabaton, who have a lot of songs about historical battles, has done a few that are clearly done from the perspective of the side they wouldn't support. The most obvious examples are Stalingrad and We Burn (the latter is about the Yugoslavian Civil War).
"Iron Man" by Black Sabbath is about a man who becomes unable to speak and then revenges mankind because of this, killing everyone. In fact, Black Sabbath only used the name "Iron Man" because the song is about a villain; otherwise they would have been sued by Marvel Comics. Of course, Marvel then licensed the song and repurposed it as a Hero Song for the movie of the same title... but making sure that the lyrics weren't there. The original title was even going to be 'Iron Bloke', except that 'bloke' is a UK slang term that wouldn't be known in America, and as such they were told to change it to something more international, hence 'Iron Man'.
"Police Truck" by the Dead Kennedys, about a group of Dirty Cops that take the title vehicle out for a night of drinking, beating up drunks and gang-raping a prostitute.
The song "Un Mauvais Dieu" ("A Bad God") from French Hip-Hop group Manau tells in it's intro the story an evil deity trapped below the earth by the druids, foretold to return at the dawn of the year 2000. The actual song is the aforementioned evil god bragging about how dark and sinful he is, and how he will bring hatred and suffering to the Earth once he is free.
The Protomen have given one to their version of Dr. Wily with "The Hounds". He spends half the song gloating about framing Dr. Light for murder. For something that seems to depict just how much of a sociopath Wily is, it's an absolute Ear Worm with a tune that one can dance to.
It also explains part one of his totalitarian state, which is "a giant screen in the middle of town everyone can see and hear, constantly barraging the populace with misinformation and propaganda." So basically, you standard dictatorship, but more high tech.
Unlike most villain songs, Wily doesn't pull this out while there's still any chance of his plan being stopped. He waits until his victory is essentially secured.
"I built a little empire out of Some crazy garbage called the blood of the Exploited working class But they've overcome their shyness, Now they're calling me 'Your Highness' And the world screams, 'Kiss me, Son of God!'"
A few more examples: "Reprehensible", "Hall Of Heads" (commonly interpreted to be about Princess Mombi (or Princess Langwidere from the book version) of Return to Oz), "No One Knows My Plan" and "I'm Your Boyfriend Now" (named after a Freddy Krueger line).
Dream Theater's "Home" from their brilliant album "Metropolis Pt 2: Scenes from a Memory" follows this trope. The song contains a section where it is revealed through soliloquy that the character named "the Miracle" is actually in love with his brother's girlfriend and is sleeping with her. He laments that despite the shame he feels, he will find a way to tear them apart so that he can have Victoria. In fact, the whole song is about the two brother's different sins while the narrator of the whole story remains oblivious to the truth. Its a powerful song.
Symphony X has an entire album of these with their latest release, Paradise Lost, unsurprising as most of the songs are from the point of view of Lucifer. Almost every single song is a Villain Song from Lucifer, with the only exception being the opening and 'The Sacrifice'.
Pain of Salvation's 2004 concept album "Be" features a few of these, most notably "Dea Pecuniae", in which the villainous character sings about how he got rich through cut-throat duplicity, before it becomes a duet between him and the very voice of his dark desires.
Many Finntroll songs are Villain songs, given that they're mostly about trolls eating people, sung from the point of view of the trolls.
I'm proud to be a glutton, and I don't have time for sloth I'm greedy, and I'm angry, and I don't care who I cross I'm Mr. Bad Example, intruder in the dirt I like to have a good time, and I don't care who gets hurt I'm Mr. Bad Example, take a look at me I'll live to be a hundred, and go down in infamy
Arguably, I Can't Decide by the Scissor Sisters, since it is Foe Yay in song form. It's about a guy who is contemplating if they should kill the person they are singing to.
Aside from The Master using it as a full-fledged Villain Song, it's also spawned a whole lot of villainous tribute videos (go search "Can't Decide" on YouTube. We'll wait).
"Villain Song" by Kirby Krackle, despite the title, is actually about a villain announcing retirement after growing tired of the hero constantly beating him. This changes in the final verse, where the villain realizes that his life just isn't the same without the thrill of constantly fighting the hero and committing evil deeds and happily proceeds to get back to active villainy.
The punk/cabaret act The World/Inferno Friendship Society have "Fiend in Wien", a raucous villain song from the perspective of Hitler about his awful youth and how he came to see the world as shit. Considering the band's main hero is Peter Lorre and they're a bunch of anarchists, it's more sarcastic than anything else.
"Lust for Timing" from The True Story of the Bridgewater Astral League is sung by the League's leader, Jon Gilch, as he gloats over his luck and apparent invincibility while heading a crime syndicate. The previous song, "Incendiarism", is sung by the League as a whole while in the process of joyfully stealing cars with the foolproof alibi of being asleep at the time. However, the musical casts the BWAL members sympathetically rather than as hardened criminals, especially in the second act.
Streets: A Rock Opera has the song "Agony and Ecstasy", which is also part BSoD Song. The villain portion represents the knowledge that drugs destroyed DT once, cannot do anything to help him, but he still longs for them.
Dead Winter Dead has two: "I Am" is human selfishness and greed turning people against each other, "Doesn't Matter Anyway" is for the Arms Dealers getting rich off the war and don't give a damn about ideology or politics of their buyers.
The Wake of Magellan has "Complaint in the System", the Irish mobsters and drug dealers have created a status quo that benefits them and will protect it.
Bigg Milt's newest rap "what's going on" is a rather strange version of this trope. Instead of being sung from the point of view of a actual person, it's actually sung from the point of the drug dope, claiming he is the real terror in the world. He says God Is Evil according to what he wrote about god in the Bible.
"Please Mr. Gravedigger" (1967 Self-Titled Album) starts with the singer sarcastically addressing the gravedigger, who's also a grave robber...but then he reveals that the reason he's been able to witness these crimes is because he keeps visiting the grave of a little girl he murdered, and he's got a grave ready for the gravedigger to go into.
"Running Gun Blues" (The Man Who Sold the World) is sung by a soldier who no longer has a war to fight, but (being Ax-Crazy) decides to just keep killing people. As the song begins, he's "cut twenty-three down since Friday".
"Sweet Thing/The Candidate/Sweet Thing (Reprise)" (Diamond Dogs) starts out as a come-on from the faux-innocent "sweet thing" before opening up into the internal gloat of the "candidate" and briefly returning to the former.
God Himself gets in on the action in Faust by Randy Newman, singing "How Great Our Lord", with a wonderfully slimy performance by James Taylor. Newman himself sings the Devil's parts; the most straightforward Villain Song from him is probably "Can't Keep A Good Man Down", where he plots to return to Heaven by winning a (heavily stacked) wager with God.
The Toadies' "Possum Kingdom", sung by a serial killer (or vampire, depending on your interpretation) to his victim.
Blind Guardian's "Ride Into Obsession" is an introduction to the two opposing main characters of the Wheel of Time series... from the viewpoint of the villain of course! Keep in mind, the quoted section is merely the opening.
"Come, I'll show you the end. You're damned, 'cause no-one can defy me! Just watch these maddened creatures, Like you they all once reached out, A war to win, But I'm gonna burn their vision down!"
Every headlining song in the Seven Deadly Sins series is this, with the main character being a villain acting out a respective sin. However, there is the notable exception of "Daughter of Evil", which strangely enough, despite using Rin's voice (Princess Riliane's actor), is told as if the audience is listening to a story about Riliane instead of Riliane herself gloating. In fact, it comes off kind of like a "The Villain Sucks" Song. And weirdly enough, it's ambiguous as to whether Evil Food Eater Conchita and The Tailor Shop Of Enbizaka are meant to be in first person.
Special mention goes to The Lunacy of Duke Venomania, where the titular Duke gloats freely about his conquest of multiple women using supernatural means.
Also Judgement of Corruption, where Judge Gallerian Marlon revels in the money he's taking from people with the biggest Slasher Smile on his face, though also highlighting his motivation (to heal his disabled daughter).
Master of the Graveyard is the Villain Song of the titular master, though sung mostly by her servants about how she eats everything.
Rush's concept album Clockwork Angels has one in "The Anarchist".
Kanye West's Power is basically about an all powerful celebrity getting off on how much people hate him. There's a remix version that's meant to be a song of empowerment by being an asshole and bragging about dumping on Taylor Swift.
Pepe Deluxé, Queen of the Wave, "A Night and a Day". The liner notes describe the subject as "a poetic synopsis" of Mainin's descent into "destroy the world"-tier villainy, and the lyrics don't suggest even a hint of regret.
Slayer's "Angel of Death", about Josef Mengele. This is far from their only example; the band has a habit of making songs sung from the perspective of Serial Killers and other lovely individuals, but it is undoubtedly their most famous.
"Your Momma says I'm evil, and I cut like a knife You cut a little deep, find the devil inside Now burn little honey, I hypnotize I'm so mean, so mean, so mean I'm so mean, so mean, so mean
I'm a motorcycle cowboy, a honky tonk junkie Fallen shooting star. Broken desperado on the wrong side of the barrel My best friend's a pawnshop guitar."
"A Criminal Mind" by Canadian artist Lawrence Gowannote currently the frontman for Styx is from the perspective of an unrepentant convict.
Michael Longcor's done several. Most notably, the epic Falconsbane -
"For I know life is never pretty - and no fight is ever fair And the power and the glory go to those with strength and flair Those who cross me never prosper, those who threaten end up dead I don't get mad - I don't get even - I make sure I get ahead!" ** But also "Valley Forge", from the point of view of an agitator calling for desertion from the Revolutionary Army in the coldest winter of the war, "Sharks of the Open Sea," an epic pirate song, and, arguably, "When Tenskwatawa Sings," which is either this or an Angry Mob Song depending on how you feel about William Henry Harrison, the 9th President of the United States -
"The French Whites came to the Shawnee tribes bringing furs to take and trade And the British gave guns and bought the scalps of Americans we'd raid Now Harrison comes by the river-side runs crying "justice" he will bring But Tecumseh speaks and the people rise when we hear Tenskwatawa sing! * Finnish proge band YUP has a song called Kuonamagneetti (Drossmagnet) on their 1994 album Toppatakkeja Ja Toledon Terasta. It is a confession song of album's big bad, Volmar Pätsi.
"Arsonist's Lullaby" by Hozier tells the story of a guy who simply is driven to set things on fire and how he got to be that way, as described from his own perspective. It may not be right, but he acknowledges that it's just who he is. As the chorus explains:
"All you have is your fire And the place you need to reach Don't you ever tame your demons But always keep them on a leash"
St. Jimmy by Green Day from American Idiot. While he's not completely a villain and really Johnny's drug fueled id, it's his grand entrance and him introducing himself.
On the other hand, Peacemaker from the following album 21st Century Breakdown is a straight villain song about the villain himself singing of his plan to commit mass cleaning of infidels. Not only the lyrics are taken out of a total villain song but the music fits perfectly for what one would expect of a villain song in a musical. Now, the identity of the villain singing isn't quite clear, but speculation goes from a radical member of society who wants to kill Gloria and Christian for daring to stand against them, to a friend of Christian who wants to get rid of Gloria for being so adamant on changing her beliefs, to Christian himself falling for the 21st Century force of change and becoming the villain, now wanting to get rid of Gloria.
Madonna has "Back In Business" from her Dick Tracy soundtrack album I'm Breathless, probably reflecting her character in the film "Breathless" Mahoney. Surprisingly, a different song called "Back In Business" appears in the movie instead of Madonna's version.
Vocaloid producer mothy does this type of song quite a bit, more particularly in the Evillious Chronicles. At least half of the Seven Deadly Sins Series is the sinner gloating about how evil they are, with Conchita from the gluttony song making a repeat performance in "Master of the Graveyard" for the Clockwork Lullaby Series.
Many, many songs by Nick Cave, from both The Birthday Party and as a solo artist. Particularly notable examples are "Deep in the Woods" (in which a serial killer gloats about his most recent murder before boasting about his general misanthropy) and "O'Malley's Bar" (in which the protagonist describes a brutal and motiveless mass murder in detail before revealing himself as a Dirty Coward when the cops arrive).
Stone Temple Pilots song "Sex Type Thing" is about a serial rapist singing about how the women he raped, asked for it because of how they dressed.
The album Preservation Act 1 by The Kinks starts with a song called "Preservation" about a corrupt leader called Flash who says that he does what he does to help people but really only does it for himself, and then goes on later to a song called "Here Comes Flash" which is just a straight-up warning of the man:
"He'll be a friend to you, be so sweet to you Then he's going to screw you, just like that. You'd better run, you'd better fly Hide your daughters, hide your wives Lock your doors and stay inside, here comes Flash."
Many Horrorcore songs are written from the point of view of serial killers or mass murderers; examples include "Darkness of Da Kut" by Lord Infamous and "Trauma" by Tech N9ne. Even mainstream rappers do this on occasion (who more commonly take on the "street thug" persona), such as Dr. Dre and Ice Cube in "Natural Born Killaz".
"Goodybe, Mr. Bond" by the band Blotto is sung by a James Bond villain ranting about how weary he is of 007 always defeating him and gloating that he is done messing around and dead set on ensuring James Bond is finished.
Nick Cave had Murder Ballads, an album of songs about murdering from the killers perspectives, and sometimes as a duet with their accomplices or victims.
The Vice Quadrant: A Space Opera by Steam Powered Giraffe brings us Necrostar, about a sort of Power Rangers/Lovecraft mashup villain. Far more awesome than it sounds.
Kids Praise: Most of the songs are praising God, a few have nothing to do with God or religion and are simply plot-related, and a couple are actually sung by the villain, Risky Rat.
Subverted with "Han Mi" from Miss Helen's Weird West Cabaret, which sounds like it was supposed to be a proper villain song about a Dragon Lady crimelord. As it progresses, though, the singer injects her complaints about the role's racist implications, then devolves further when she realizes that she's never interacted with the writer and doesn't even remember her life outside the cabaret show, which makes her question if she's losing her mind.
Theory Of A Deadman have a number of songs about how much of a jerk the lead singer is, though the most obvious example is "Villain", where he proclaims that he's the villain of the story and that people are more interested in him than heroes.