In Rick Veitch's early-2000s run on Aquaman, the titular hero confronts his archnemesis (and murderer of his son), Black Manta, and, after defeating him, uses his new magic powers to re-wire his brain and cure him of his autism; the painful and incompetent treatment he received as a child was part of why he'd become such an insane monster. He appears to turn himself around, but the apparent Freudian Excuse and Heel-Face Turn are subverted when, at a critical moment, Manta stabs Aquaman in the back and explains: "Y'see, deep down, in my most secret heart of hearts, I'm still a totally depraved sonuvabitch whose main goal in life is to watch you die. Slowly and painfully. Just like your kid."
During Dark Reign, Marvel Comics introduced Zodiac, a guy who killed every single member of an old supervillain team with the same name so he wouldn't be confused with them. Zodiac plots about the fall of Norman Osborn. Why? Because he finds Osborn's new position an insult to all who just wants to commit evil for it's own sake, like himself.
Darkseid openly admits to being an evil god and that he desires to crush all happiness and free will in the Universe.
Set, apparent leader of The Order in Invincible spinoff Guarding The Globe. In an issue released the same week as the issue in which Contagion makes the speech above, Set begins a meeting of The Order with this:
I've heard it said, everyone is the hero of their own story. The thought is that even the most vile villain believes his actions to be right and thinks of himself as "good". I am here to tell you, right now, that I am evil. I am greedy, selfish, I do not care for the plight of others.
The Joker once identified himself to Black Canary as "genuine, card-carrying, lock-me-up-throw-away-the-key lunatic!" It sparked a letter column debate (remember those?) about whether or not insane people could recognize themselves as being insane.
The Joker has been shown several times to be fully aware of being crazy. The plot of Alan Moore's classic The Killing Joke hangs on that very fact.
In Judge Dredd, Pa Angel is openly trying to raise his sons to be the "meanest, orneriest, baddiest bunch a' men that ever lived." The boys are only too happy to learn from him.
Kid Miracleman/Marvelman displays this trope when he goes over the edge. Moments after starting his slaughter-spree, he spares the life of a nurse who had been kind to him. He returns a moment later, saying "They'd only say I was going soft...", and pulverises the top of her skull with a blast of his eye-beams.
I'm older'n you. I'm ninety years old. You want to know how I look so pretty? I take drugs. Special H.A.T.E. drugs. Life-extending drugs. H.A.T.E. has the best drugs because H.A.T.E. loves me. And I love H.A.T.E. Every day of my horrible drug-extended terrorist-fighting life. Every day I smoke two hundred cigarettes and one hundred cigars and drink a bottle of whiskey and three bottles of wine with dinner. And dinner is meat. Raw meat. The cook serves me an entire animal and I fight it bare-handed and tear off what I want and eat it and have the rest buried. In New Jersey! For H.A.T.E.!
Herr Starr of Preacher starts out as a Knight Templar, but, in the end, admits, however unrepentantly, that he's become a "monster" obsessed with hatred and revenge.
Ava Lord from the Sin City story "A Dame to Kill For" identifies herself as evil in her Evil Gloating speech to Dwight McCarthy, who she has just manipulated into murdering her husband Damien so that she can inherit his money:
Ava:Insane? Ha! That's so easy, so convenient — and so wrong. Crazy people push shopping carts down the streets and talk nonsense. Crazy people sit in padded cells and soil their pants. A madwoman couldn't have pulled this off. No. There's a word for what I am, but nobody uses it anymore. Nobody wants to see the simple truth. If they did, they'd kill people like me as soon as we revealed ourselves. But they don't. They close their eyes and blather about psychology and say that nobody is truly evil. That's why I've won. That's why I always win.
In the very first issue of Sonic the Hedgehog, there is a sign on Robotnik's desk which reads "Dr. Robotnik: Supreme Dictator, Industrial Polluter, Megalomaniac, Corrupt Politician, Underhanded Reprobate, Rain Forest Ravager, Puppy Kicker, Oil Spill Coordinator, Holiday Hater, Insurance Salesman. Rights violated while U wait!"
Supreme's arch-enemy Darius Dax delights in being evil for the sake of being evil.
In Transformers Generation 2, Starscream ends up begging Optimus Prime to take the Matrix back, as he doesn't want to be good!.
Contagion, the villain of the first arc of Wolverine: The Best There Is.
I am not the hero in my own story. I am the bad guy. I have no end in mind that justifies my means. There are no skeletons in my closet, no abusive childhood or inciting misery that might expiate my vile behavior. Nor am I insane. I know the difference between good and evil. And I am fully capable of empathizing with the pain, emotional or physical, of others. No sociopath, I. Rather, I simply prefer bad over good. Wrong over right. Dirty over clean. Sick over healthy. Untrue over true.
The film version of X-Men avoids this by having Magneto simply call his group "The Brotherhood of Mutants".
Similarly, recent issues of Savage Dragon have subverted this a bit with the new Over Lord referring to his team (the Vicious Circle) simply as The Circle. Since there are a number of similarities between Magneto's Brotherhood and Over Lord's Circle, it's arguable that one is in response to the other.
In the comics, one version of the Brotherhood working for the US Government and led by Mystique takes a smart idea and calls itself by the innocuous moniker "Freedom Force".