A Song of Ice and Fire has many complex antagonists with very understandable motives. However, there exist several characters who are, indeed, total monsters.
Despite his young age, King Joffrey Baratheon stood out as one of the vilest characters in the series. While always shown to have a darker side, Joffrey finally crossed the line when he had Ned Stark executed, ensuring that the war with the Northerners would never reach a peaceful conclusion. Joffrey not only did this in front of Ned's daughter, Sansa, Joffrey's own fiancée, he then forced her to look at the decapitated heads of her father and household afterwards. This was then followed by a long period of Domestic Abuse during which Joffrey had her regularly beaten by his Kingsguard and threatened to rape her even after she married his uncle, Tyrion. As king, Joffrey reveled in his power over life and death, and his reign was filled with all manner of pointless cruelties. Joffrey's crimes included having a minstrel whose song offended him choose between losing his hands or his tongue, attempting to have a drunken knight drowned in a cask of wine, firing on starving peasants with his crossbow, ordering his bodyguard to cut through a crowd of peasants to get at one of them who threw manure at him, nailing antlers to the heads of Stannis sympathizers and firing them from trebuchets as entertainment during the Battle of the Blackwater, and attempting to convince his grandfather to execute everyone who fought against him, regardless of whether or not they surrendered. A budding psychopath who believed being the king gave him the right to do whatever he liked, Joffrey's sadism was so great that he was well on his way to surpassing his predecessor as the next Mad King of Westeros.
Ser Gregor Clegane, alias The Mountain That Rides. An eight foot giant kept in a constant state of rage due to migraine headaches, Gregor is one of the most feared characters in the setting, and with good reason. He is rumored to have killed his sister when they were children, to have arranged for his father's Hunting Accident, and to have murdered both of his wives. The things that we know he did are even worse. As a twelve year old boy, he burned off half of his younger brother Sandor's face when the latter dared to play with one of Gregor's toys—a toy that Gregor himself, it should be noted, did not want anymore. At seventeen, he dashed the baby Prince Aegon's head against a wall, and then raped and murdered his mother, Princess Elia, with her son's brains still on his hands. At a tournament at the start of A Game of Thrones he kills one of his opponents, and tries to kill another, and that's before he's turned loose on the countryside. He and his men proceed to rape and murder anyone who falls into their hands, often torturing people to see where they have hidden their gold. At one point in A Clash of Kings each day, for ten days, Gregor picks one person from a group of villagers and has his Torture Technician, "the Tickler", question that person over and over, until they die from the torture. One of the villagers, a mother, volunteers to be taken if they will spare her daughter. The next day, he has the daughter questioned too, to make sure the mother didn't leave anything out. Another time he smashes a girl's face in for speaking when he wanted silence, than turns her over to his men to be gangraped for days. When confronted by the brother of Princess Elia, who repeatedly asserts that "Her name was Elia of Dorne. You raped her, you murdered her, you killed her children," Gregor's only concern (besides killing him) is that the man has gotten the order of events wrong.
"Her name was Elia of Dorne. First, I killed her screaming whelp. Then I raped her. Then I smashed her fucking head in. Like this."
Ramsay Bolton is possibly the worst of all Complete Monsters in the series — and by the end of ADWD, he has arguably surpassed Gregor Clegane and Joffrey. How does he manage this? Well, he skins people alive for his own amusement (his whole family has a thing for this, actually; a flayed man is their symbol), hunts down women on his father's feudal lands, and rapes them when he catches them. Once he’s finished, he kills them, then skins them - if they’ve given him good sport. If they haven't, he begins with the flaying. He also tortures captives into insane and broken shells of their former selves, eager to obey him. His signature method is to strip the skin off their fingers and let the exposed flesh fester until the victims beg him to cut their fingers off. And if they bite their own fingers off and rob him of that pleasure, he flays another finger as punishment. Before he rose high enough to enjoy his sports properly, he also had a penchant for raping girls, killing them, and forcing his servant to rape the corpses.
Craster, a particularly vicious Wildling and ally of the Night's Watch (each of whom identifies him as belonging to the opposing organisation), who in his own words, kneels to no man, including Mance Rayder, King-Beyond-The-Wall. Living alone in a huge, ramshackle compound, Craster keeps a harem of women in line with brainwashing and violence, breaking their spirits until they cannot rise up against him, despite the fact that they vastly outnumber him. All of these women are his "wives"; many of them are also his daughters and granddaughters. When one of them becomes pregnant, Craster waits to see if it is a boy or a girl. If the child is female, he waits until she is old enough (read eleven or twelve) and does his best to impregnate her. If the child is a boy, Craster leaves him in the woods to be killed by the cold or devoured by the Others; this way they cannot challenge his control over the women. Obsessed with his own hedonism, and raising the next generation of wives, Craster uses his alleigance with the Night's Watch to make sure that nobody, not even the Watch, interferes with his business.
Hoat's company, the Brave Companions, are a bad lot, but noselesspaedophiliacserial rapist and serial killer Rorge is acknowledged in-universe and out as the worst of them. Freed from the Black Cells under King's Landing, along with his companion, Biter, Rorge signs on with the Brave Companions after Arya Stark saves him from certain death. He offers to repay her by anally raping her with her own wooden sword, only stopping when she threatens him with Jaqen H'ghar. He later goes against Hoat's own orders when he tries to rape Brienne of Tarth, and tortures the recently crippled Jaime Lannister by kicking him in his stump, when Jaime reminds him that Brienne is supposed to remain unharmed. It's after Hoat's death, though, that Rorge really comes into his own. Taking control of a gang of brigands, he burns down the town of Saltpans, in an act so savage that it shocks the sensibilities of a Westeros long inured to the atrocities of Gregor Clegane and Vargo Hoat. Killing twenty men himself, Rorge rapes every woman and child in town, most notably raping a six year old girl while wearing chainmail; he also rapes nuns before feeding them to Biter. Upon encountering Brienne again, he expresses a desire to "cut off her legs and set her on her stumps so she can watch me fuck the crossbow girl." The girl in question is under ten years old. Sidematerials would indicate that he is also the reason why Biter is the way he is—finding an orphan boy, Rorge removed his tongue, filed his teeth, and made him fight dogs with only his new fangs. A consummate Woman & Child Hater, and a serial predator in a world full of warriors, Rorge earns the enmity and disgust of everyone he meets.