Alex DeLarge of A Clockwork Orange happily rapes, murders, and beats as he pleases. Why? Because, as he freely admits, he just prefers to be evil.
House Bolton in A Song of Ice and Fire. Their house arms features a flayed man due to their history of flaying their prisoners alive. They wear pink and red capes because ages ago they used to wear the skins before submitting to House Stark. Their castle is called the Dreadfort. Lord Roose Bolton and his heir Ramsay commit numerous atrocities and eventually betray their liege lords in a massacre that shocks the continent.
Partially subverted in the Babylon 5Expanded Universe trilogy The Passing of the Techno-Mages with Galen, whose original high ideals for the Technomage order are shattered when he finds out that Technomages are products of Shadow technology. As such, he starts to believe himself to be inherently evil, incapable of good. Turning into a Person of Mass Destruction doesn't help. He later changes his mind.
On the other hand, several other Technomages definitely fit the trope. Razeel willingly chooses to serve the Shadows for an unknown reason. Circe's motivation for betrayal is pure desire for power.
Various characters in Andrew Vachss' Burke books, including the AntiVillain Protagonist himself, identify themselves as "thieves". How evil these characters are actually varies from person to person.
Lieutenant Colonel Korn from Catch-22 takes positive delight in describing how odious and reprehensible his plans are.
Colonel Korn(to Yossarian): I really do admire you a bit. You're an intelligent person of great moral character who has taken a very courageous stand. I'm an intelligent person with no moral character at all, so I'm in an ideal position to appreciate it.
A rare case of this trope being played both seriously and non-Narmfully is the Hunter of C.S. Friedman's Coldfire Trilogy. Living in a world where the human mind can unconsciously shape reality, he has made an absolute monster of himself in a bid to deliberately invoke the trope of the invulnerable evil overlord.
Beyond that, he's getting his immortality through a pact with an entity that's the unholy lovechild of Satan and Cthulhu - if he ever stopped being knowingly and extremely evil, it would withdraw its end of the bargain, killing him.
Invoked by Sinistrad of The Death Gate Cycle as a form of Obfuscating Stupidity. He is legitimately evil and power hungry, but played up the "stereotypically evil villain" role (including the very act of changing his name to "Sinistrad" in the first place) so that his fellow wizards would dismiss him as a harmless eccentric (coupled with marrying an idealistic young wizardess who was infatuated with him in order to make it seem like he really wasn't so bad under his sinister exterior). This directly lead to the other wizards deciding he was no threat, allowing him to blackmail his way to their leader before the majority caught on to what was happening.
Subverted in the Discworld novels with Lord Vetinari, who cheerfully classifies himself as one of "the bad people", but is actually a force for good, or at least stability. A sort of Card Carrying Anti-Villain.
Greenyham: You can't do that! Vetinari: Can I not? I'm a tyrant. It's what we do.
Greenyham has been calling Vetinari a tyrant through most of the book, on the grounds that Vetinari runs the government. (Vetinari probably is a tyrant in the original Greek sense of the word: a guy who bosses the polis.) It's a Take That to libertarian propaganda.
Note that he also classifies everyone as "bad people". But some of them are on opposite sides.
Lady Felmut, in Wyrd Sisters. Granny Weatherwax tries to Mind Rape her by "showing her her True Self" - and it doesn't work, because she's already well aware she's a villain, and she's proud of it.
Also somewhat subverted with Dr. Hix (né Hicks), head of UU's Department of Post-Mortem Communication. Because necromancy is a so-called evil curriculum, he wears the skull ring and forces himself (if apologetically) to take an Evil stance on things, simply because it goes with his job description.
Done something with by Abrim, The Grand Vizier in Sourcery. He points out that the evil things he does are expected of him. But he doesn't apologize for doing them, like Dr. Hix, or do them for the greater good, like Vetinari. Probably closest to lampshaded.
The Last Hero gives us Evil Harry Dread, a Dark Lord from Cohen the Barbarian's age, who, like Cohen, has become disgruntled with how the world's become. When he tips off the gods on Cohen's quest to deliver fire in the form of a high-explosive, he justifies it by saying, "Well, I AM Evil." He seems to treat being Evil like a career, doing things that are expected of villains, and at the same time purposely making the usual mistakes- stupid guards, easily escapable jails, uniforms that can be used to go undercover with- and feels deeply hurt when today's do-gooders BLOCK OFF his escape tunnel to subvert Exit Villain Stage Left.
Dies the Fire by S.M. Stirling. The Big Bad who's turned Portland into a feudal dictatorship uses the Eye of Sauron on his flag. One of the protagonists comments how stupid this is, as it would make more sense to use the Stars & Stripes to give himself legitimacy. When his colleague points out that "Hey, it's cool to be bad!", he responds "What's the point of letting people know you're evil enough to backstab them at the first suitable opportunity?"
In the Incarnations of Immortality series, Satan seems to be the Corrupter. And, he is very good at his job — to evoke the latent evil in souls. Interestingly, in For Love Of Evil, we find he is a good man and according to Archangel Gabriel he is one of the most effective Incarnations because he has not become Drunk with Power.
In the same book, Satan himself says he was impressed with Zane, but protocol required him to depart in an angry huff.
In Death: some of the bad guys reach this level in the series. Casto from Immortal In Death admits that he is a selfish man. Reanna Otts in Rapture In Death cheerfully describes herself as a sociopath and completely agrees with that diagnosis!
Don John in William Shakespeare's Much Ado About Nothing comes right out and says it. He's pissed that he can't rule because he's a bastard son, and will therefore do anything so long as it causes his brother grief: "I had rather be a canker in a hedge than a rose in / his grace, and it better fits my blood to be / disdained of all than to fashion a carriage to rob / love from any: in this, though I cannot be said to / be a flattering honest man, it must not be denied / but I am a plain-dealing villain." Played quite straight by Keanu Reeves in the 1993 film, the character has no purpose but to foil the good guys.
In the Rainbow Magic series, Jack Frost is this. He causes trouble just because he can, and loves seeing bad things happen to others.
Some of Redwall's villains clearly revel in this trope. Vilu Daskar, upon being praised by his crew for inventive sadism, modestly says "Oh, I do my best to be the worst." The trope gets even more obvious in Triss, when the villainous pirate crew does three song and dance numbers dedicated to their own gruesome behaviour. The irony here being that Grubbage, one of the singers of the second song ("'Tis nice to be a villain/wot all honest creatures fears/and terrorise the beasts for miles around"), does a Heel-Face Turn in a sadly very brief skimmed-over epilogue.
Acheron Hades of the Thursday Next series wrote the book Degeneracy for pleasure and profit and extols the wonder of doing evil for its own sake. He also complains that profit "dilutes the taste of wickedness".
The Astronomer from the Wild Cards universe could have been created as an exercise to write a character as utterly evil as possible. He seeks to rule the world. He revels in murder, rape, corruption and both psychological and physical torture. He has no value system, no passions, no vision, no motivation other than his personal power and pleasure, and he never tries to explain or justify his acts in any way. His previous life is a blank book, and the reader never has any occasion to understand what made him what he is. He is so cold, ruthless, calculating and devoid of any sense of humour that we can't even merely categorize him as "crazy". He has no respect for neither his allies not his enemies, and will readily use, abuse and kill even his own allies. And to people he knows, he will casually admit all of the above, including sacrificing his own allies, while both scaring and manipulating them in such a way that they go on serving him while knowing they have every chance of being betrayed.