Adaptation Displacement: To mainstream audiences, the TV show based on the books is far better-known than the books themselves. And the title Game of Thrones has far more name recognition than A Song of Ice and Fire.
Viserys seems to be set up as a major villain, but he dies halfway through the first book, before he or any of his supporters set foot in Westeros.
Khal Drogo is set up as a major threat to all of Westeros but is reduced to a catatonic state after a festering wound is 'treated' by the blood magic of a maegi who had reason to despise him. He never even crosses the narrow sea to begin the invasion of Westeros.
Renly plans on stealing the throne from Stannis and has put together the largest army in Westeros, but he's assassinated on the night before the battle without putting up a fight. Stannis takes the bulk of his forces into his own campaign against the Lannisters.
Balon Greyjoy declares himself King of the Iron Islands and has set up a major campaign to raid the North, but dies off-page before he ever does anything. His brothers, however, take up the cause.
Tywin, as head of the Lannisters and chief adversary for many of the other characters, but his death has nothing to do with his domination of the continent. His abuse of his son Tyrion finally catches up to him and he dies an ignominious death on a privy.
Anvilicious: Numerous characters come down hard on romanticized songs and histories, which turn complicated and often downright ugly situations into simple and idealized stories with clear moral lessons of dubious authenticity. Characters who take these stories too seriously end up suffering terribly for it. On top of all that, most of the singers and minstrels who spread these tales are themselves portrayed as sleazy and unsavory. Singers are also on the receiving end of Cruel And Unusual Deaths and in the case of the Blue Bard, Cold-Blooded Torture.
Daenerys' prolonged arc in Essos. While it teaches her many useful lessons about effective rulership and politics, it has many readers tearing their hair out waiting for the dragon battles already!!
Remember how there's supposed to a Zombie Apocalypse of some kind with the coming of the Others? Five books into a seven book series and so far they haven't even reached the Wall. And given the large gap between books...
Daenerys spends the first three books building herself into an active conqueror. However, she spends most of A Dance With Dragons comparatively inactive and out of her depth. Her army is getting whittled away by rebels, her dragons are locked away, she's forced into a sham marriage and she's distracted by lust for Daario.
Theon Greyjoy, to the point where it's easy to forget he was ever a badass. It's worth noting that he was a skilled archer, fought beside Robb Stark and conquered Winterfell with a handful of men. However, this is partially justified, given that he is horrifically mutilated by Ramsay Snow.
Darkstar. Though he's disliked by a lot of the fandom for being an admitted attempt to recapture the popularity of Oberyn Martell, some readers enjoy the air of mystery surrounding him and his somewhat hilarious charisma.
Some fans find Catelyn Stark to be unsympathetic due to several of her rash decisions, such as arresting Tyrion and freeing Jaime. Others find that her Mama Bear motivations make her more sympathetic or simply don't see her flaws as a impediment to their enjoyment of her character.
Daenerys Targaryen is a polarizing character, especially by Dance with Dragons. While many fans enjoy her chapters and her character, others complain about her Plot Armor and find her teenage infatuation with Daario Naaharis to be Romantic Plot Tumor.
Cersei Lannister, because her status as a Big Bad Wannabe is really divisive among fans - is it a good depiction, or is her utter political incompetence cartoonish? Many fans wish that we'd gotten a look into her mind at an earlier point (as when she gets a Sympathetic P.O.V., she's started Jumping Off the Slippery Slope), and that she were a bit more competent (or at least allowed a chance to gain legitimate victories); many non-fans wish the same on the competence front, if only because reading about her complete and utter stupidity gets grating after a point and ADWD is the only book were she doesn't appear prominently (unlike some other divisive characters). There are many perspectives in-between regarding this woman, and few people can agree on the best possible interpretation of her character - and that's after you've decided whether she should be pitied, hated, admired, etc.
Broken Base: The fanbase was actually a pretty contented one up until the publication of A Feast For Crows. With A Dance With Dragons finally out, the new broken base seems to divide between fans who love it and consider it a return to form, and those who hate it and consider it AFFC 2.0. And then there are those who loved AFFC and don't consider the idea of AFFC 2.0 to be a bad thing. The split in the fanbase seems to be a result of the increased focus on world building in AFFC and ADWD. Westeros and Essos are presented in more detail than ever before, but parts of the fanbase consider this to have occurred at the expense of plot.
Common Knowledge: It's widely known across the internet and it was joked about in films such as Logan Lucky that George R.R. Martin in general, and ASOIAF in particular takes too long to publish because the author writes too slowly. This is because of the lengthy Schedule Slip between Books 3-4, Books 4-5, and Books 5-6 (which is still TBD six years and counting).
As some commentators [noted, that in terms of word count, ASOIAF is much bigger than other series, making the challenges of writing it and completing it quite different from other series. For point of comparison, J. K. Rowling conceived and completed Harry Potter in about the same time, Martin conceived the series. But the total word count of the complete Harry Potter series (1990-2007), is around 1,084,170 words, averaging 63,774 words per year. However, by the time GRRM published A Dance with Dragons (Book 5 in a projected seven book series), Martin had hit 1,770,000 words, averaging 88,500 words per year. This is only counting the main series and not including Tales of Dunk and Egg, Archmaester Gyldayn's Histories, The World of Ice & Fire, the four episodes of Game of Thrones whose screenplay he had written, his other work as editor and contributor to Wild Cards and the many other promotional interviews he has done since the greater demand that came with his greater fame and profile on account of the series (which he did admit slowed down the progress of the sixth book but which will likely be a Doorstopper of the same nature as Book 5).
John Scalzi: "Shorter version: During those years the unsocialized were snarling at Martin for being lazy or procrastinating or indolent or whatever, he wrote about as many words for novels as I had. By this superficial but easy-to-quantify metric, on the novel front he was as productive as I was, and most people seem to agree that Iíve been pretty productive these last six years. I just spread my words around five novels while he poured all of his into one."
Counterpart Comparison: Littlefinger can be compared with Heathcliff from Wuthering Heights. Both fell in love with a girl they were fostered with (or the closest thing to love), only for her to push him away by marrying someone of her station. Littlefinger/Heathcliff amasses large sums of money and begins to take his revenge on those who kept him from the girl he cared about.
Though it has its share of likable characters, readers find the bloodshed of the setting to lose its impact over the course of the series. One can only hear so much about all the raped women and skinned children and random murders and how utterly assholish everyone seems to be before they lose interest. The fact that the first book spends quite a long time establishing that the Stark family is one of the very few major players with any honour worth speaking of and constantly contrasts this with their honourless - and usually far more successful - rivals, paired with the first hundred pages or so being dedicated to smashing this family to tiny pieces, doesn't help new readers.
The infamous "Red Wedding" is a notorious invoker of this trope - while being an effective plot twist, it pretty much cuts the whole House Stark storyline that was developed from the very first book, which brings the question if it's worth the time investing into any other character's story arcs.
Littlefinger is wildly popular, despite being one of the most scheming and villainous characters in the series, and in many ways the Big Bad of the story (or one of, anyway). It helps that he's quite witty as well as described as stylish. More than one fan has even expressed a wish to see Littlefinger come out on top in the game of thrones.
Ramsay Snow, the Bastard of Bolton, often gets this treatment from fans, although in his case at least some of it is tongue-in-cheek, partially because he is so over-the-top evil.
Brynden "Bloodraven" Rivers gets this mostly because he looks like Elric and for possessing both Valyrian and First Men abilities. Fans usually gloss over the fact that Rivers let thousands die during the Great Spring Sickness while devoting most of his time on a feud with Bittersteel, as well as using magic to convert Westeros into a Police State. He can be seen as a Well-Intentioned Extremist, as his ruthless methods seem to have been necessary.
Many characters will do anything to get into Cersei's bed, including abandoning any sense of morality they might have to earn her physical favor. Even as she becomes less and less likable throughout the series, she is still one of its primary sources of erotic fanservice.
Fanfic Fuel: Westeros' history has drawn a lot of attention from fanfiction writers, particularly Robert's Rebellion, since there are a lot of fascinating events and people but not much detail. In fact, there are plenty of mysteries that the characters themselves are still puzzling over. Not to mention the accounts from various characters contradict each other or are blatantly biased, so everyone seems to have their own idea about how the everything really happened.
Sansa/Sandor (called SanSan), easily the most popular single pairing in fandom.
Arya/Gendry ended up very popular, in large part due to Gendry being a rare kind and decent person who Arya spends a lot of time with, that their trusting friendship is one of the few bright spots in both their lives and that GRRM writes them with romantic elements. The History Repeats element of the pair befriending each other as commoners being an inverse of the failed Lyanna/Robert Arranged Marriage also helps.
Lyanna/Rhaegar, even though they've both been dead for almost twenty years. Fueled by the abundant theories about the willingness of their relationship and any child begotten by them. Though, considering how the relationship ended, the ship does leave a bad taste in the mouths of some.
Jon/Daenerys is also extremely popular, even though to date they have never met and Dany may not even know that Jon is alive. (And also, of course, by the most common fan theories, Dany is Jon's aunt, though given her family's marriage practices this may be more of an argument in favor of the pairing than one against.)
When Sam and Gilly make love on the Cinnamon Wind, his penis is described as a "fat pink mast".
Cersei and Taena's lesbian sex scene is utterly killed when Cersei calls Taena's pubic hair a "Myrish swamp".
During one of Jon's sexual encounters with Ygritte, he's "as hard as the rocks around them".
Cersei and Jaime having sex in a sept next to their son's dead body while she's on her period is a pretty infamous scene.
Right after Dany finishes a ritualistic bath in Vaes Dothrak, Drogo has sex with her in front of everyone (the Dothraki don't have a taboo against public nudity or sex, but still). "Three quick strokes and it was done." Really?
Maesters earn silver chain links for mastering the field of medicine. Silver is known for its antibiotic properties, and it has a history of medical use in various real-world cultures.
At one point in A Dance With Dragons, Stannis's army is marching to rescue the supposed Arya Stark. One of the knights asks if all of the trouble is worth it for a woman; this is a reference to The Iliad. The knight who responds to this comment is nicknamed "Middle Liddle," which is also the nickname of a commonly used lexicon of Ancient Greek.
House Martell rules the Moorish Spain analogue of Dorne. In the real world, Charles 'the Hammer' Martel was the Frankish king who fought to keep the Moors from spreading beyond the Iberian peninsula.
The Tyrell family are responsible for Joffrey's death. One of the characters Joffrey is based on is the Prince in the Tower Edward V. Sir James Tyrrell was a man who apparently confessed to murdering them.
Since the series is heavily based on the Wars of the Roses (with the Stark and Lannister families standing in for the Houses of York and Lancaster), a few small details will seem particularly meaningful if you know the Wars better than most. Case in point: the central conflict in the series is called "The War of the Five Kings" as a subtle nod to the fact that the Wars of the Roses spanned the reigns of five different kings from competing dynasties (Henry VI, Edward IV, Edward V, Richard III, and Henry VII).
As the series goes on, it gradually becomes clear that the Tyrells are meant to be stand-ins for the Real Life House of Tudor, with their name, their rose emblem, and their uneasy alliance with an ambitious Queen Regent. If you know your British geography, you might notice that the position of the Tyrells' home realm in Westeros corresponds perfectly to the position of Wales in Britain. The Tudors were originally a Welsh family, with "Tudor" being an anglicized variant of the Welsh given name "Tewdwr".
In addition to this, there are all sorts of subtle references and meta-commentary to obscure and famous historical incidents and persons. Deciphering it has proven to be an Unconventional Learning Experience for readers in Ancient and Medieval European History.
I Am Not Shazam: Ever since the show came out and generated more interest in the books many people have ventured into libraries and bookstores asking for the "Game of Thrones Books". Of course, newer printings of the older books and all new books have "Game of Thrones, The Hit Original Series From HBO" stamped on them now, anyway.
In AGOT, the deaths of Eddard and Robert, Robb is proclaimed as King Of The North and North effectively seceded against Iron Throne, Joffrey, Myrcella and Tommen are offsprings of Queen Cersei and her twin brother, Joffrey become king and the fact that Dragons are reborn.
In ACOK, Pycelle helped the Lannisters sack the capital. Winterfell being sacked. Lack of Robert's legitimate heir used to justify his 2 brothers' claim to the throne, North and Iron Islands separately seceded and thus the start of Civil War Also Huge number of denizens north of The Wall try to cross it.
In ASOS, we learn that Jaime killed The Mad King to save the realm. There's also the Red and Purple Weddings, deaths of Oberyn Martell, Tywin Lannisters, and Gregor Clegane, white walker and wight are real, are approaching Seven Kingdoms along the long winter and both are reason Wildlings try to cross The Wall and Catelyn comes back as the vengeful, zombified Lady Stoneheart.
AFFC: The Martells are plotting against the Iron Throne and Tommen becomes king with Cersei as the real power behind him.
In ADWD, Rhaegar's son Aegon is very much alive. The Children of the Forest aren't extinct.
Daenerys Targaryen, whose ships include: Dany/Drogo, Dany/Jorah, Dany/Jon, Dany/Aegon, Dany/Handmaidens, Dany/Tyrion, Dany/Viserys, Dany/Daario, Dany/Robb, Dany/Quentyn, Dany/Victarion, Dany/Asha (or Yara, as this is particularly popular with show fans), Dany/Loki, Dany/Damon Salvatore, etc.
Sansa Stark is also a biggie with: Sansa/Sandor, Sansa/Tywin, Sansa/Willas Tyrell, Sansa/Tyrion, Sansa/Aegon, Sansa/Harry the Heir, Sansa/Petyr, Sansa/Jon, Sansa/Jaime, Sansa/Tommen, Sansa/Margaery, Sansa/Pod, etc.
Arya Stark with: Arya/Gendry, Arya/Jaqen, Arya/Jon Arya/Edric Dayne, Arya/Aegon, Arya/Robert Baratheon, Arya/Willas, Arya/Tywin, Arya/Jaime, Arya/Hound, Gendry/Arya/Aegon, etc.
Jon Snow with: Jon/Ygritte, Jon/Val, Jon/Dany, Jon/Theon, Jon/Robb, Jon/Aegon, Jon/Sam, Jon/Jaime, Jon/Arya, Jon/Sansa, Jon/Catelyn, Jon/Satin, Jon/Alys, Jon/Jeyne Westerling, Jon/Jeyne Poole etc.
Aegon Targaryen with: Aegon/Dany, Aegon/Arya, Aegon/Sansa, Aegon/Jon, Aegon/Margaery, Aegon/Arianne, etc.
Ned Stark with: Ned/Catelyn, Ned/Robert, Ned/Lyanna, Ned/Ashara Dayne, Ned/Wylla, Ned/Cersei, Ned/Jaime, and even Ned/Margaery.
Robb Stark with: Robb/Dacey, Robb/Roslin Frey, Robb/Jeyne Westerling, Robb/Myrcella, Robb/Margaery, Robb/Jaime, Robb/Roose, Robb/Sansa, Robb/Theon, etc.
Theon Greyjoy has been shipped with: Theon/Catelyn, Theon/Roose, Theon/Ramsay (Yes, really), Theon/Asha, Theon/Myrcella, Theon/Jeyne Poole, Theon/Jeyne Westerling, Theon/Arya, Theon/Stannis, Theon/Barbarey Dustin, Theon/Cersei, etc.
Like You Would Really Do It: Although the books have a reputation for Anyone Can Die, few fans really bought either that Brienne had been hanged (for one thing it would have made her preceding story an infuriating Shoot the Shaggy Dog), or that Jon Snow had been Killed Off for Real. Though the exact fate of the latter has yet to be confirmed, his story is too important to the Myth Arc to be ending just yet. The show, at least, confirms he gets better.
Joffrey. One of the biggest douches in the series, but so very fun to loathe with a passion.
A more amiable example would be Tywin Lannister, who generates admiration because of his badass aura and his history of being a rather effective battle commander and leader, who can keep a leash on Joffrey. He's of course balanced out for his cold attitude and his unfair treatment of his son Tyrion.
Randyll Tarly became the fandom's answer to the Chuck Norris Facts fad. Tarly is a fairly tough customer in the series, but nothing close to the level that fans playfully describe him.
Jaime Lannister is known within the world as one of, if not the best, swordsmen around. The 2010 suvudu.com "cage matches" between fictional characters drew a large contingent of supporters for Jaime, who bested Hermione Granger and Cthulhu, among others, before facing off against The Wheel of Time's Crystal Dragon Jesus, Rand al'Thor. Martin wrote short descriptions of how he thought Jaime would win, which usually relied on Tyrion providing him a gameplan.
Wyman Manderly has attained this status (with praises that sound almost Chuck Norris-esque, e.g. "Lord Manderly is a vegetarian. Meaning, he does not eat Freys until first he puts them into vegetative state with his fists."). His earned badassery comes from the fact that everyone underestimated the fat jolly man, and that he had the audacity to feed Frey pies to people like Ramsay and Roose Bolton without them even suspecting, and even having the bard sing "Rat Cook" right to their faces without them realizing anything, and finally surviving his throat being cut.
Rickon Stark is more of a Memetic Future Badass. He's by far the most aggressive Stark, despite being the youngest, has the most savage direwolf by his side and is living on an island of cannibals that everyoneis afraid of with a wildling spearwife. Many fans expect him to grow up to be a fierce warrior who'll wipe out all of House Stark's enemies and might even become the next King in the North.
Memetic Loser: Gerold "Darkstar" Dayne is regarded this way by a good portion of the fanbase. This stems partially from his rather cheesy name, appearance and persona, with lines like "I am of the night" seen as trying too hard to invoke Evil Is Cool, crossed with the fact that for all his boasting and buildup as a badass the only thing of note he does is try to kill Myrcella Baratheon (an unarmed and harmless little girl), a task which he fails at. This has led to his nickname "Dorkstar" and general perception as a whiny, pretentious Emo Teen and incompetent poseur with an over-inflated opinion of himself.
GET HYPE FOR CLEGANEBOWL, the long-anticipated showdown between Sandor Clegane and Gregor Clegane, the latter of whom is speculated to be an undead puppet and the mysterious Kingsguard Robert Strong; taking into account that Sandor is probably a gravedigger of all things lends to a showdown of poetic justice.
Blatantly ridiculous fan theories like "Euron is actually Benjen, who is actually Rhaegar, who is actually Mance" or "Lightbringer isn't actually a sword, it's just what Azor Ahai called his penis." "Benjen=Euron=Daario" in particular is bound to be brought up every time one of the characters is mentioned.
Tywin Lannister crossed this line before the beginning of the series: When his son Tyrion fell in love with a thirteen-year old orphan, he lied to Tyrion that the girl was a paid whore and forced Jaime to lie as well. Tywin then had his entire garrison of soldiers brutally gang-rape the poor girl, forcing Tyrion to watch it alland then participate. The minute Tyrion learns the Awful Truth, he flies into a murderous rage and brutally kills Tywin since this for him was the absolute last straw. The fact that it turns out that Tywin was a lying hypocrite who had sex with Shae (Tyrion's girlfriend) makes his actions even more monstrous.
Theon Greyjoy has perhaps the most notable one. Starting as something of a Jerkass with a downtrodden history that made him sympathetic, Theon crosses the line in a shocking way. His most heinous deed is when he allows Ramsay Bolton in the guise of 'Reek' to kill miller's two young boys, and spiked their tarred heads to his gate to cover up the escape of Bran and Rickon Stark. And then A Dance with Dragons, using some of the best writing in the series, manages to bring him firmly back into the sympathetic category again because of the horrific tortures he receives from his captors.
Roose Bolton crossed the line years ago by raping a peasant woman when she refused to sleep with him. The result? Ramsay.
The Red Wedding caused much of House Frey to cross the line, especilly Walder Frey. He orchestrated the massacre out of spite and laughed while it happened (not to mention that murdering a guest under your roof is considered one of the most despicable and dishonorable things a person can do in Westeros). However, the mastermind behind the Red Wedding was Tywin Lannister, and Roose Bolton was also involved, but both of them had already crossed the Moral Event Horizon.
What Gregor did to Princess Elia and her baby. Even worse is that he laughs about it and was only 17 at the time. Also, he held his little brother's face in a fire because Sandor played with his toys. It's also hinted that Gregor killed his father, his little sister, and his first two wives. He once even killed a man for snoring too loudly!
An in-universe example: several characters consider Jaime Lannister's killing of Aerys Targaryen to be this. Since Jaime himself thinks it's his Moment of Awesome (with considerable justification, given that Aerys was planning to burn down the entire city of King's Landing with its residents still inside), this causes friction. A example is throwing Bran Stark out of a tower window because the boy saw him having sex with his twin sister.
If Cersei had not long since passed the MEH, her treatment of Falyse Stokeworth would see her leaping across it. She tells Falyse and her husband to get rid of Bronn, and when the plan fails she condemns Falyse to be tortured to death by Qyburn without a second thought simply because her presence at court would inconvenience Cersei.
Varys crosses it when he murders Kevan Lannister to deliberately destabilise the realm. Regardless of his supposed good intentions, he's dooming thousands more to die, even though it's supposedly for the realm's good.
Years ago, Rorge took in an orphan boy. He proceeded to file the lad's teeth and force him to fight dogs until he went insane. You know that boy as Biter.
One of the most chilling MEHs of the novels comes when we find out what happened to RamsayBolton's wife: he forced Lady Hornwood to marry him so he could take her lands, then locked her in a tower with nothing to eat. They found her with no fingers and blood around her mouth. Ramsay may have crossed it before the series began, when he poisoned his legitimate kind-hearted brother Domeric so he could become their father's heir.
Aerys II "The Mad King" seems to have crossed it when he burnt Lord Rickard Stark to death while his oldest son Brandon was Forced to Watch and strangled to death. Brandon had threatened to kill Aerys' son for kidnapping his sister, but it was still horrific what Aerys did.
Randyll Tarly either crossed it by threatening to arrange a Hunting "Accident" on his own son unless he joins the Night's Watch, or even earlier in the backstory, by chaining said son to a wall for three days straight for daring to want to become a Maester.
The way George RR Martin tries to write the sounds of things like war horns (HAAAAAAAARRROOOOOOOO).
Long-winded descriptions of food and clothing. Particularly when it seems like not a single meal can be described without a mention of grease running down chins or into beards.
The combination of archaic phrases with more modern language annoys some readers. For example, "break your fast" instead of "have breakfast" and the intermittent use of "four-and-twenty" structure for numbers.
George also begins to humorously misuse the adjective "wroth" as noun in later novels when he talks of "God's wroth" or "Ramsay in his wroth". The noun he was looking for is actually "wrath." (Basically, if you can substitute "anger" use "wrath", if "angry" use "wroth.") It seems even excellent authors can fall victim to Delusions of Eloquence.
Viserys' warnings about "waking the dragon". Fair enough, it would be frightening from Dany's perspective. From the reader's perspective, he's too obviously a little shit to be frightened by. It doesn't help that he uses the phrase nearly every time he appears, and by the end he sounds more like he's trying to turn it into his catchphrase than actually threatening anyone.
Theon names his ship Sea Bitch.
In a scene from the fifth book, Dany hears Quaithe talking to her in the stars, telling her "Remember who you are." It can't possibly be taken seriously when the same thing happens, word for word, in The Lion King.
Also, in ASOS, Stannis and Melisandre talk about "waking the great stone dragons" on Dragonstone... just like the Ancestors wanted Mushu to do in Mulan.
Darkstar's introduction to Myrcella in A Feast for Crows is "Men call me Darkstar, and I am of the night." You can't help but giggle that line because it blatantly came from a certain Dark Knight who is obviously way out from that loser's league.
Lady Stoneheart sounds like the name of an evil stepmother from a fairy tale, or worse yet, a Care Bears villain.
The long, unnecessarily detailed description of Daenerys suffering from diarrhea as a result of dysentery in A Dance With Dragons, which is so disgusting that it wraps back around and becomes hilarious. It's reached Memetic Mutation status with some fans, with the passage describing it becoming something of a copypasta used to mock the series on the internet.
There are other moments in the series where Martin's prose leaves much to be desired, especially in regards to the many sex scenes, which can become Fan Disservice as a result. Among other things, there's a description of a penis as a "fat pink mast", a character's vagina described as a "Myrish swamp", and a scene where a character's sexual ecstasy is summed up with the line "her cunt became the world". Outside of sex scenes, there's also a line where a ship caught in a storm is described as groaning "like a fat man straining to shit", which is just a bizarre simile, and not the sort of thing you want to be picturing at that moment (or ever).
The Dothraki like to get drunk on fermented mare's milk, a custom taken from their real-world counterpart culture (see kumis). Unlike real-world kumis and other dishes that appear in the books, the reader is given no reason to believe the drink is appetizing in any way, and it's described as being just as sour-smelling, lukewarm, and chunky as you would think.
The dishes at the Red Wedding are either bland or just revolting (jellied calf's brains?!).
In-Universe example: Jaime Lannister is forever known as the Kingslayer for murdering the man he was supposed to protect. To be fair, while the King in question was popularly recognized as The Caligula, the fact that most people don't know just how off his rocker Aerys was (planning to burn the capital to the ground out of spite), and the misperception that Jaime killed him to further the ambition of House Lannister (Ned, in fact, believes that he killed Aerys because he wanted the throne for himself and was just playing a long game), is what really circles this trope off.
Fandom Example: Catelyn Stark, despite being a kind and caring mother who gives her eldest son solid advice and a woman with a strong sense of honor and duty. She is widely disliked because her first actions in the series are against the extremely popular Jon Snow and Tyrion Lannister. Against Jon, she is openly disdainful generally. She tells Ned on no uncertain terms that she not allow Jon to remain in Winterfell because he is his son, not hers, after Ned leaves for the South. This anguishes Ned, who had hoped Jon would stay at Winterfell with Robb as they are so close. Maester Luwin comes and reveals Jon that wishes to join the Night's Watch. And in a moment of mad grief over her comatose seven-year-old son Bran, she tells him "it should have been you" before breaking down in tears. Soon after, upon meeting Tyrion Lannister at an inn, she arrests him for the attacks on Bran, mistakenly believing him to be the one responsible. This arrest serves as one of many catalysts that sets the long simmering tensions in Westeros aflame, erupting into the War of the Five Kings.
Similarly, Sansa Stark will apparently always be vilified for her personality and actions in the first book, with the Break the Cutie induced Character Development she undergoes in the later books apparently either ignored or said to not be enough to ever excuse an 11-year old girl for her past mistakes. In particular the Trident incident - where she refuses to corroborate Arya's truthful story about Joffrey attacking her and her friend Mycah, which leads to Mycah's and Lady (Sansa's direwolf) being killed - is held against her for a very long time, and is almost always used in anti-Sansa arguments even years after the fact. note Though the fact that Sansa in-universe also blames Arya for "getting Lady killed" and takes a long time to admit it was actually Cersei and Joffrey's fault doesn't help.
Ramsay Bolton's very... fond of his Reek. This only makes being Reek even more terrifying, if that's even possible.
"And what do you want, my sweet Reek?" Ramsay murmured, as softly as a lover. His breath smelled of mulled wine and cloves, so sweet.
Also, in early books, Littlefinger's stroking Sansa's face, commenting on her attractiveness, saying he understands Joffrey wanting the "sweet prize" of her body, squicked out many fans. After book three, he's too obvious about his attraction to her for it to count as subtext, but, now that he's her uncle and passing her off as his daughter, it's even creepier.
"Very well, ser. Bring on your storm. And remember, if you will, the name of this castle."
Archmaester Marwyn, called "The Mage" by the other archmaesters for his interest in the occult and jumping at the call to put his knowledge to work.
Septon Meribald and the Elder Brother in A Feast For Crows for being genuinely believable, flawed but good priests, and for the War Is Hell speeches given by both which is considered by many to be some of the best writing in the entire series.
Wyman Manderly's granddaughter Wylla, who stands up for the Starks and gives Davos her support, despite her family's protests and attempts to silence her. Lord Wyman praises her bravado once he reveals his plan to Davos.
Lyanna Mormont, who doesn't even get an actual scene. One letter to Stannis from the ten-year-old daughter of Bear Island refusing to bend the knee, and she is everyone's hero.
Alys Karstark receives a lot of fan enthusiasm for her take-charge attitude. By fleeing her Evil Uncle on horseback, she avoids a forced marriage, and by entering a bold arrangement with the Magnar of Thenn, she stands to inherit Karhold with a house full of free folk backing her.
Opening a Can of Clones: The Faceless Men; just look at the WMG page. This despite the fact that the only use of Actually a Doombot the series has so far pulled off was actually Melisandre's doing. This also seems to be based on an earlier understanding of Faceless Man powers that was jossed in A Dance With Dragons: The Faceless Men keep around faces taken off of corpses and use blood magic to put them on their own faces. While this doesn't necessarily rule out impersonation via glamour, chances are that if a Faceless Man impersonates someone, the person they are impersonating is dead.
Rewatch Bonus: The highly elaborate history of Westeros is an epic in itself. You just won't be able to fully appreciate it until you've read the books many times over.
Romantic Plot Tumor: Dany's teenage crush on Daario is one of the most frequently complained about things in A Dance With Dragons.
The Scrappy: A few examples, with a cast so large. Some are due to characters having intentional flaws, while others are simply disliked as characters.
Dany's Meereenese supporting cast in A Dance With Dragons is very unpopular for a variety of reasons - difficult names, perceived blandness and the idea that the conflict in Meereen is ultimately irrelevant. Daario Naharis draws particular ire for his negative effect on Dany's character.
Prince Aegon Targaryen, primarily to Dany's fans due to his brattiness compared to Dany's maturity (at a younger age, no less), as well as him coming completely out of nowhere and going to conquer Westeros before Dany can. Plus, he has a much more solid claim to the Targaryen throne than Dany does, which Dany's fans feel ruins the value of her being the last Targaryen. To put this into perspective the prevailing fan theory before his appearance was that he secretly survived despite his alleged murder by Gregor Clegane. When he finally did appear, the prevailing theory was that yes, he did die, and this "Aegon" is a fake.
Seasonal Rot: A Feast for Crows features only half the usual characters and places a lot of emphasis on new characters, giving the reader more of a commoner's perspective of Westeros than before. Many readers rejected the shift in emphasis, preferring the focus stay on the main plotlines and characters.
Ship Mates: When it comes to Crack Pairing, Sansa/Domeric and Myrcella/Robb are often shown side-by-side. Either way, Joffrey doesn't get anyone.
Ship-to-Ship Combat: In-universe example with the Rhaegar/Lyanna/Robert mess. Although Rhaegar running off with Lyanna was seen as a catastrophic situation all round, there are differing opinions over the couples. Robert, Brandon Stark and their supporters were obviously Robert/Lyanna shippers who thought he and Lyanna were in love and that Rhaegar kidnapped and raped her, while Rhaegar's supporters were more sympathetic to Rhaegar/Lyanna, saw the Prince as a romantic who developed mutual feelings for Lyanna and perceived them as Star-Crossed Lovers. Meanwhile the Martells supported the Rhaegar/Elia match and were furious that Rhaegar abandoned his proper wife and got her killed. Notably, Ned - one of the few people who may have got Lyanna's perspective - is aware that Lyanna never loved Robert, that Robert never properly knew Lyanna and speaks highly of Rhaegar despite everything.
For Sansa: Sansa/Jaime, Sansa/Willas, Sansa/Stannis, etc.
Jon Snow and Daenerys might be the biggest one, as many fans feel they fit the "Ice and Fire" motif.
Aegon/Young Griff and about a dozen females he's never met.
Squick: The series is known for its grittiness, gore, and creepy sex scenes. Often the squick is played for black humour.
A disgusting but completely hilarious scene is when Jaime and Cersei Lannister have rough sex next to their son Joffrey's tomb. While Cersei bleeds from her period. Their incestuous relationship already brings a certain amount of squick to any sex scene.
Cersei describes how she got a kick out of eating Robert's semen as a figurative consumption of tens of thousands of his potential children out of spite. Weird.
Tywin Lannister in the end of book three is shot in the gut with a crossbow while sitting naked on the privy, and takes a postmortem dump. Tyrion later suggests that shit was dripping from the wound. Later on, due to dying from a gut wound, his body decomposes faster than normal and is getting rather ripe by the time of his funeral, and the smell nauseates everyone there.
Littlefinger and his creepy obsession with Sansa Stark, which is wrong on so many levels.
Theme Pairing: It has been (pretty convincingly) argued that Brienne and Sansa would be pretty much perfect for each other, as Sansa has not completely given up on the concept of a "true knight", and Brienne is exactly that. The characters have yet to meet, though.
They Wasted a Perfectly Good Character: Jeyne Westerling. As a girl from the Westerlands marrying and falling in love with the young King in the North, she had a lot of potential characterization to be explored, but the book just drops her by the wayside following her introduction and lets Robb die because of their marriage without developing their relationship. Later on, after the Red Wedding, it's explained that her mother Sybelle Spicer was working with Tywin by using Jeyne as a pawn to instigate the Freys' betrayal of Robb. The most we get out of her is her saying "I loved him" and the books fail to show how much being used as a destabilizing tool affected her.
They Wasted a Perfectly Good Plot: Arianne's chapters had potential to be a very interesting arc, but it was foiled so quickly that many feel that there was really no point to her story.
Walder Frey's decision to collaborate in the Red Wedding in the way he did. In the process he's joined sides with two backstabbing houses and taken most of the blame for the atrocities committed there. Although House Frey gained a big jump in nominal power, it's also received a bad reputation throughout the kingdom, so bad that killing Freys became a new fashionable sport among various rebels and resistance members. Some fans believe that the cons vastly outweigh the short-term gains that his house has received.
Many of Eddard Stark's actions in Game fall under this, but worst was preemptively telling Cersei that he knows her secret and what he plans to do, all while having reason to believe that Cersei had his foster father killed for the exact same reasons.
Woobie Family: Between deaths while giving birth, to being betrayed and slaughtered by their "allies", to being Forced to Watch all that, and going from riches to absolute rags, the Starks have seen it all.
The measurement systems used in the original English version are normally adapted to equivalent ones used in ancient times by the target language.
Other than that, foreign Western translations avoid changing too many of the terms used in the book (e.g. honorifics) and keep them as they are in the English, because Westeros has a distinctly English flavor to it.
One particularly botched and narmy attempt at Woolseyism is one of the Russian translations. Calling Winterfell "Zlozim'ye," Dreadfort "Ostrog Uzhasniy" and Casterly Rock "Bobrovyi Utes" (Beaver Rock) (thinking "Casterly" refers to the Latin word for beaver, not to the House of Casterly who built it), yet keeping the Anglo-Saxon sounding names of the characters caused an unpleasant salad of languages. In the most well-known Russian translation, only those place names are translated which are clearly just plain English words, such as "the Twins" or "King's Landing".
The Danish translation is slightly better, though very boring. It translates all the names into Danish, but due to there being less Danish words regarding castles, many of them have similar names. Winterfell and Riverrun become Vinterborg and Flodborg respectively, literally "Wintercastle" and "Rivercastle". The Eyrie becomes "the Eagle's Nest" which works, but just makes the other translations seem stupid in comparison. King's Landing becomes "Kingsport", which seems to have been meant to evoke the Danish capital Copenhagen, whose Danish name literally is "Buyersport".