Claggart in Billy Budd. He's described as being "naturally depraved" and he wants to destroy the hero so badly (without a reason) that he provokes the boy into killing him, just to be sure he'll be hanged.
Smaug in The Hobbit. He is the inspiration to the Chaotic Evil Red Dragons, and is greedy, avaricious and wild, not being involved in any social structure.
Mr. Jonathan Teatime (pronounced Teh-ah-tim-ah) in the novel Hogfather. Other Guild Assassins take professional pride in inhuming the target with no collateral damage to bystanders, whenever possible, but to Teatime, killing is art for art's sake.
Pratchett also has the elves, who are both vicious and incredibly chaotic. They want to invade the world so that they can have fun by hurting people.
Lacrimosa de Magpyr in Carpe Jugulum is the permanently teenaged daughter of the Count de Magpyr. Whereas the Count is Lawful Evil and wants to rationalise vampirism, she has no patience for all that and just wants to kill everyone who gets in her way and do violence for fun.
Randall Flagg from The Stand. Although Flagg's Las Vegas might be Lawful Evil (due to the day to day operations being run by Lloyd Henry), Flagg himself is a creature of whim, delights in causing trouble where none exists, and is ultimately self-destructive.
Patrick Bateman of American Psycho offers an interesting case of a blood-crazed Chaotic Evil individual essentially camouflaging himself in a Lawful or even Neutral Evil environment (that is to say, Wall Street), where his dead-eyed narcissism and rampant, violent misogyny are simply par for the course.
Fenrir Greyback in Harry Potter, whose sole objective in life is to turn as many children as possible into werewolves... Or kill them, whichever strikes his fancy.
Bellatrix Lestrange is this compared to the rest of the Death Eaters. She's wicked and crazy, who enjoys her work of torturing and murdering a little too much. Voldemort himself admires her bloodlust, holding her chaotic nature in high regard.
The In-Universe alignment of Fate/Zero's Caster (Gilles de Rais, aka Bluebeard). Just look at how he does things in the Holy Grail War. His Master, Ryuunosuke Uryuu, isn't much better.
Morgoth from The Silmarillion: according to Word of God, his ultimate goal is simply to smash creation down into dust, into the primal darkness from which it came. By contrast, his lieutenant (and occasional Dragon) Sauron is Lawful Evil.
Ungoliant is a massive spider-like Eldritch Abomination motivated solely by her never-ending Horror Hunger. Teaming up with Morgoth, she poisoned and killed the Two Trees of Valinor after drinking their holy light. After the two fled Valinor, Ungoliant betrayed Morgoth and sought to eat him after he refused to give her the Silmarils, the last fragmnets of the light of the Two Trees. Morgoth barely survived, relying on his Balrog army to chase her away. For the rest of her days, she would eat whatever she could catch, breed with monsters to create more hideous spider creatures (including Shelob), and cause havoc and misery wherever she went. She was eventually driven to the deserts of the south, where her hunger got so all-consuming she ate herself and died.
Acheron Hades of the Thursday Next series is this. Like the Joker, he's the type who, depending on his whim of the moment, can vary between laughable, cartoonish villainy and brutal evil. For instance, although his plot to destroy great works of literature is more of the former, he's also depicted slaughtering an entire room of police officers for the fun of it.
The four protagonists, as well as lots of briefly mentioned characters in the Marquis de Sade's The 120 Days of Sodom, and probably many characters from his other works, who commit acts of unspeakable cruelty, sexual and otherwise, against others for the sake of their own enjoyment. There's a reason Sade was the inspiration for the term "sadism."
Rupert of Hentzau of The Prisoner of Zenda is a very calm and calculating version of it. Rupert is the swashbuckling hero (a classic example of Chaotic Good) turned evil, and so he goes about things like treachery, casual cruelty, and attempted rape with great charm and joie de vivre.
Vargo Hoat and The Brave Companions, better known as the Bloody Mummers, the most vile, depraved, sickening mercenary troop in all the known lands. As mercenaries, they know no loyalty to a flag or cause; their loyalty is bought, and thus they serve the fabulously-rich Lannisters. However, they surpass the usual evil of average mercenary bands with the sickening things they do in the Riverlands. They firmly place themselves on the "chaotic" side after they betray the Lannisters for the Boltons, killing their own allies, seizing Harrenhal, cutting off Jaime Lannister's hand as a statement of power to his father Tywin. Stupid Evil They did all of these things in an attempt to drive a wedge between the Lannisters and the Boltons. Ironically, they are unaware that the Boltons and Lannisters are cooperating with each other, and after they have outlived their usefulness, Tywin sends Gregor Clegane and the Mountain's Men to annihilate their leadership, leaving the few survivors as fragmented bandits]].
Gregor Clegane is about as Chaotic Evil as they come. Whether it's killing children, or massacring civilians during wartime, or his decision to have an innkeeper's daughter gang-raped by his men just because, you never know what Gregor's going to do, just that it will be as abhorrent as possible. An interesting variation of this trope, as despite his tendency for reckless violence and vile atrocities, he is unflinchingly loyal to Tywin Lannister, mostly because Tywin excuses his actions. His company of bannermen, the Mountain's Men, is worse than the Mummers — while Vargo's band are all sorts of monsters and weirdos gathered from faraway lands, Gregor's bunch are just ordinary soldiers and thugs. They brutally defeat and torture Vargo's band in the later books.
Westeros will occasionally offer up a Caligula King to make the people as miserable as possible and give the characters an excuse to start a civil war. Mad King Aerys and Joffrey Baratheon are the two notable examples, both sadistic Ax-Crazy psychopaths who infuriated their nobles into rebellion by having prominent members of major Houses executed for no good reason.
Ramsay Bolton, son of Roose Bolton, is quite possibly the most evil character in the whole series, being the sort of man who flays people alive for fun, and enjoys the finer things in life, such as rape, murder, torture, and a whole mess of other atrocities, and becomes so repellently evil that his own father (no stranger to atrocious behavior, himself) expresses disgust at his methods. (Though this is more due to the negative publicity Ramsay brings on the whole House.)
Although he isn't this alignment in most adaptations of the work, the original Fantômas was a poster-boy for the alignment. Fantômas had an inspiration from Gentleman Thief characters like Arsène Lupin, but his only interest was in spreading terror and his wacky schemes involved killing people in sadistic ways (i.e. spreading a plague).
Fats Wall from The Casual Vacancy is a textbook psychopath and one of the more realistic portrayals of this alignment.
Lord Foul, the Big Bad of The Chronicles of Thomas Covenant. His ultimate goal is to break out of his cosmic prison and be free, but that can just happens to be a planet. It is heavily implied that even if he had no chance of breaking out, he would still kill and/or torture everyone on the planet just for the hell of it.
Edward Hyde from The Strange Case of Dr. Jekyll and Mr. Hyde is not only Henry Jekyll's embodied evil side, but more specifically an expression of his lower, uncontrolled desires.
Many of the Big Bads from Redwall are such. For instance, Ferahgo the Assassin divides his time between warring against Salamandastron, berating his son Klitch for his failed schemes, scaring the living crap out of his troops, employing a Master Poisoner to starve every beast on the mountain, and leaving freshly orphaned (by him) infants to die from exposure. All with a charming smile.
The Dresden Files: The entire Red Court of Vampires are petty, backstabbing bloodsuckers to the point where their own treachery sabotages their war effort. They are only loosely held together by threat of punishment and threats from either other supernatural powers or the highers-up in their own society.
Polonius Lartessa of the Knights of the Blackened Denarius is outright described as this In-Universe in contrast to her Lawful/Neutral Evil husband Nicodemus Archeleone. While Nicodemus likes to play The Long Game, Tessa focuses instead on actively spreading suffering and misery in the present, capitalizing on moments of mass panic and chaos to bring about the most damage.
Winter Lady Maeve of the Sidhe ignores her duties and is a spiteful, unpredictable brat whose cruelty reaches the point of unnecessary evil.
Codex Alera has Steadholder Kord from the first book, Furies of Calderon. Kord is a hedonistic sociopath who runs his titular steadholt as a Wretched Hive. It's frequently shown throughout the story that he has absolutely no care for what happens next or how self-destructive his own actions are - All he cares about is ensuring his own short-term success and enacting revenge on the main protagonists (Tavi and Isana) for mildly insulting him.
The Elric Saga has the Lords of Chaos, monstrous and malevolent entities that delight in suffering and are opposed to the forces of Law.
Stormbringer, the iconic sentient sword of demonic origin, is a treacherous and manipulative being, chaotic evil to the core, that hungers for blood and souls and wishes to break the Cosmic Balance. As a consequence of its influence, it caused every person who wield it to become self-destructive mass murderers and it considers the souls of its wielder's loved ones to be a delicacy.
Satan is portrayed this way in Paradise Lost. "Better to reign in Hell than to serve in Heaven". He eventually admits that he was happier as a servant of God than as the ruler of demons, but still refuses to even attempt to redeem himself because he refuses to submit to the will of another entity. Despite being essentially a monarch, he's not really Lawful Evil as he is never shown making demons follow any rules or ordering them to do anything. Satan's main concern is not having to obey anybody; whether anyone else obeys him doesn't really matter.
Most depictions of Don Juan (aka Don Giovanni) are this alignment. He's a pure hedonist who seduces, uses and occasionally murders people, with no thought beyond his own immediate satisfaction.
Literature/Wings Of Fire features Queen Scarlet, who glories in watching gladiator fights, would jump at any opportunity to cause or witness pain, and has absolutely no qualms about killing children.
Lawful Evil and wants to rationalise vampirism, she has no patience for all that and just wants to kill everyone who gets in her way and do violence for fun.