England: In canon, he's a snarky Tsundere who has had his days of pillaging and plundering as a pirate and frequently gets into fights with America or France, but is more bark than bite and clearly has a softer side (he's not called a Tsundere for nothing, after all), is more Vitriolic Best Buds than outright enemies with America and France, and suffered (and probably still is suffering) from heartbreak due to the one he cared for the most leaving him. In fanworks, one side of his Tsundere personality is all too often exaggerated at the expense of the other - and when said exaggerated side is the 'tsun', he becomes a Manipulative Bastard who only cares about himself, his empire, and/or forciblypossessing his object of desire. Becomes especially bad if Russia is made into the Draco in Leather Pants opposite of him, or America is woobiefied into an innocent and helpless victim.
Some fans also flanderize the complex issues surrounding the US atomic bombings and occupation of Japan at the end of WWII into "America is a Bespectacled Bastard Boyfriend or psychopathic Yandere who abuses/rapes a weepy, horribly traumatized Japan". How this sadist!America and traumatized!Japan could ever have become the good friends they're canonly shown to be before and after WWII (not to mention the good allies they are in real life) is a mystery.
While not always used to demonize him, the fandom also has a tendency to give America traits/flaws that don't make any sense whatsoever. For instance, High School A.U.Slashfics sometimes depict him as an Armored Closet GayJerk Jock who can't stand public affection with other guys. Compare that with canon!America, who unhesitatingly leaped to glomp England for offering him ice cream and once nonchalantly suggested that he and Japan take baths together (as in, get in close physical contact with each other while completely naked) to save money on water bills.
Really, the fact that he gets along well with Greece, should be enough proof all on its own that he's not some sociopathic bastard who cares only about himself. It also can't be a coincidence that almost all fanworks that invoke this trope with him the hardest never even mention Greece in passing relation to him and that the few Dark Fics that do mention Greece have Japan ultimately be sympathetic or at least show some redeeming traits.
China: For some other fanworks, you can swap Japan and China's names in the above "Bastard Boyfriend / Yandere" sentence and have it be just as accurate a description, but with even less justification. Yes, real-life China isn't exactly a bastion of human rights, but real-life nation =/= Hetalia nation-tan, especially when said nation-tan is a quirky and sympathetic panda lover. A nagging, old-fashioned, clingy China who treats his younger siblings like little children and except for Korea drives them away from him when he tries to help them or unintentionally embarrasses them with his old man behavior is canon; a Yandere China who abuses/beats up/rapes Korea, Vietnam, Taiwan and Hong Kong into submission during either Imperial or Red times, used to abuse Japan in every possible way (and preferentlysexual ones) when he was a kid and/or heartlessly approves of the massacres of either his own or other nations's citizens by any of his governments is not.
Romano/South Italy: Apparently, the fact that he's got a Hair-Trigger Temper and feels like The Unfavorite in comparison to Veneziano/North Italy makes him a Bastard Boyfriend towards Spain who needs to be "saved" by France (Him showing genuine concern for Spain in canon when the latter fell ill? Surely you jest!). His harshness towards his younger brother is also occasionally ramped in fandom, going as far as to have him portrayed raping Veneziano to "keep him in check" or out of jealousy of his talents.
This is so bad sometimes that there recently was wank about it on the Hetalia kinkmeme. A well-known Romano basher who thinks "he is abusive in canon towards Spain" has been accused more than once of spamming it with either Romano-bashing comments or requests in which she asks for fics where Romano is killed or beaten up for abusing Spain. Much lulz and facepalms were had.
It had infamously been brought up again in the comments to a Spain/Romano fill that included "Romano as a closeted homophobe". The prompt requested for a story in which Romano, a closeted homosexual, would be homophobic and treat homosexual nations horribly as an extension of his own self-hatred. The author was handling the very "dangerous" prompt tastefully, and yet when she reached the point in which Romano "exploded", many fangirls started demanding for him to be punished/beaten/killed/etc., creepily equalling Romano's fic behavior with real life gay bashing, saying that Romano is an homophobe in Hetalia canon, etc. And whoever tried to break in and didn't kiss these overprojecting fangirls's butts was accused of being an homophobe and hating gays in Real Life. Sigh, seeing it gone was a relief. Though due to the amount of negative reception and fans feeling any punishment the author would give Romano would never be enough (and that she planned to give him a happy ending after he worked through his problems), it appears the author abruptly discontinued the story afterwards, leaving readers hanging.
Unfortunately, the Romano bashing has appeared again on the kink meme in the form of anons who claim that it's illogical for Spain to care about Romano because Romano acts so mean and horrible to him or that he cares about Romano only because he's a saintly Love Martyr and anyone less than a saint would have seen Romano for the unworthy bastard he is. In either case, they demonized Romano's Tsundere behavior as proof that he's utterly undeserving of Spain's time and attention and dismissed the signs of care and affection he's shown for Spain in canon as unimportant because he wasn't direct or clear enough with them (apparently, saying "Wa...wait for me! I'll do something about this, but I'm not promising anything!" isn't direct/clear enough) while making excuses for Spain's own faults and the times when he wasn't really helpful with Romano's feelings of inferiority or insecurity. Cue eyerolling by many other anons who pointed out that all these claims were essentially just attempts to prove that Romano is an asshole who hurts sweet innocent wonderful Spain who is NEVER EVER responsible for anything he does.
Becomes especially ridiculous when you consider that the only canon "evidence" these fans can dredge up for Romano being physically abusive towards Spain is that he peed on Spain's house (which was entirely Played for Laughs)... and that's it. Romano's often sarcastic and short-tempered with Spain but the only time he has been shown to use actual physical violence against him was a head butt when Romano was a child (because Spain was unknowingly touching his erogenous Idiot Hair) and even his Hair-Trigger Temper tends to be limited to grumbling about Spain's weird habits but still going along with them, like when he complained loudly about turtles invading his house but didn't really do anything to stop Spain from cooing over them. Heck, Norway strangles Denmark at least twice in canon and pretty much all fans agree that this is just for humor or Tsundere purposes and not an actual sign of abusive behavior; why can't Romano's comparatively mild behavior towards Spain be viewed in the same light?
Veneziano/North Italy: On the other hand, the more rabid Romano fangirls tend to blame Veneziano for everything that went wrong with Romano's life and demonize Veneziano to make his older brother look better. It's hardly N. Italy's fault that Romano is screwed up in the self-confidence department, and he actually does care for Romano and shows it. And making him into a Psychopathic Manchild to woobify Germany (who of course is completely blameless of his country's WWII misdeeds) and have Prussia rescue him? Does not compute.
An example of the rabid Germancest hate against Italy is here. It's on Mediafire since image sites kill it, but it's worth the download since it shows the butthurt and the batshit in a simply priceless way.
Turkey bashing shows up in some Spain/Romano fics, stemming from a canon incident when Turkey kidnapped a young Romano, who was then rescued by Spain. Some authors push it too far, however, and make him seem genuinely evil and often with a gross obsession with Romano, often portraying him as cruel and abusive so Spain can swoop in to save Romano and show how pure and caring he is by contrast.
His treatment of Greece in numerous fics takes the cake, however. Greece abused as a kid or teen by Ottoman Empire!Turkey? Turkey raping Greece because he wants to teach him a lesson or can't control his urges anymore? All par for the course in Turkey/Greece fics, to such an extent that Greece sometimes gets caught up in this trope too, turning from a patient, laidback Kindhearted Cat Lover who gets snippy only with Turkey to an angry, violent man who's bitter towards the entire world and has no patience for anybody he thinks is stupid (which includes nations other than Turkey), just so that the fanwriter can show how his relationship with Turkey is not a Destructive Romance, even when Turkey is treating him worse than he ever did in canon, because Greece's always been like that and/or Turkey is the only one he shows his sweet side to. There is not enough room on this page to describe everything wrong about that.
Prussia: More than one fan has taken his Small Name, Big Ego, Butt Monkey and Bad Ass traits, used for comedy in the series, to all kinds of extremes. As a consequence, many fics and RP scenarios have Prussia derailed into either:
A) a Card-Carrying Villain who rapes and beats his allies and friends to keep them terrorized and under his thumbs (if he's not eating Jewish children for the lulz - yeah, that was mentioned in a really infamous RP log) and is to blame for all the German World War II atrocities while his younger brother Germany is merely "misguided by his bosses" or yet another victim of Prussia's abuse. Which, you know, completely ignores how lots of the Nazi resistance groups came from the ex-Prussian territories, among other stuff;
B) an absolutely brainless Jerkass whom every single European country hates to death, who stuffs himself with beer, only exists to make dumb jokes and act like a Troll without showing any good personality traits, and whose presence WILL make Hungary go automatically frying pan crazy before he can even breathe in her surroundings.
France: Yes, France is a Lovable Sex Maniac whose treatment of the nation-tans often skirts Black Comedy Rape. Yes, he can be shallow and whiny and often sucks at fighting. Yup, he can be quite the Manipulative Bastard if he wants. And yeah, he and England don't get along. However, that does NOT give fandom a pass to flanderise France into an absolute moron who only thinks with his dick, a heartless rapist who lacks any character depth and must be shot to death so he won't tie up and brutally rape the whole cast (despite how France actually denies being a rapist in canon), or a slutty Smug Snake who toys with a teen!America's feelings and insecurities (and maybe, even his body) during The American Revolution purely to spit on and laugh in the face of a Purity Stufied England who is never ever to blame for his own actions or decisions.
Spain: He is a really strange case. While Romano often gets bashed to Hell and back for being supposedly "evil and abusive" to him, he's more often than not played as a helpless and ultra-innocent woobie whose own flaws "can't be helped" and "should not be taken in account". There are some fans, however, that gleefully insist that Spain MUST actually be a Yandere or a Cute Psycho in canon, taking incidents in which he's shown not-so-nice sides that are actually Played for Laughs and blowing them WAY out of proportion.
Also, out of all the fics portraying Spain's Conquistador or Civil War days, it's highly likely that many of them will have Spain as a Yandere rapist/abuser towards his OC colonies or fellow canon nations. While the majority take the Bastard Boyfriend route, others definitely play it as this trope, and the Unfortunate Implications just can't be uglier.
And then there are the fics that portray Spain as a pervertedpedophile who regularly tries to rape the young kid Italian brothers/America/one of the old Spanish colonies/etc...
Austria: While not a super obvious case like others, there's enough evidence to put him here. The Austrian Empire has had a war-full story and the relationships with other nations (France, Hungary prior to the Austro-Hungarian Empire, Spain, etc. and especially Italy) were very conflicted, yep, but that's barely an excuse to portray him as being a Domestic Abuser who regularly beats, rapes, whips, tortures and executes Hungary and North Italy. He was already a harsh Stern Teacher in canon, and yet he still did Chibitalia's work for a day so the kid would have some time alone after HRE left the manse - that's enough proof of how Austria is more complex than he looks.
There's also a very pervasive fanon that accuses Austria of having forced Hungary to put on dresses and physically/sexually/mentally abusing her during the times she served at his mansion and/or during the Austro-Hungarian Compromise. First of all, it's never mentioned who exactly told Hungary to get her Girliness Upgrade, as the strip treating the days around Hungary's arrival to Austria's mansion only shows Hungary in a dress by the end but never explains who's behind the idea. Second, Austria treats Hungary with far more deference than he does with young!Italy on screen. Third, Hungary willinglyprotects Austria in chronologically posterior strips and Austria allows her to do so, something that a Domestic Abuser wouldn't be likely to do. Fourth, Hungary and Austria are still in excellent terms after their off-screen divorce and she still willingly protects him if needed. And yet many fans still bend over to say that Austria the character mistreated Hungary the character, using "historical canon" as an excuse and reducing the very complex historical matters behind the Austro-Hungarian Compromise to "Austria was a monstruous and cruel rapist/wife beater and Hungary was a weak baby unable to stand up to him!"
Canada: Oh yes, believe it or not, even the sweetunassertiveNice Guy is not immune from this treatment. As mentioned above, many of Canada's rabid fangirls have a terrible habit of putting his brother America down in order to glorify him into a Sympathetic Stu. This phenomenon has reached a point where it's actually costing Canada popularity points with annoyed circles in the Hetalia fandom. In particular, a good number of America fangirls who are sick of seeing America colored up as a Jerk Jock to make Canada look like a saint have issued their own retaliation. Usually, they'll exaggerate Canada's Beware the Nice Ones moments (such as that one time when he seriously chewed America out with a three hour long "The Reason You Suck" Speech) and turn him into a full fledged emotionally and verbally abusive Bitch in Sheep's Clothing, or in some cases outright Ax-Crazy (mostly with a hockey stick, but at least one incident involved a chainsaw). While Canada does indeed resent his brother at times, he is shown to still care for him to some extent and their relationship is more or less normal between brothers (even if it is a little vitriolic, it's mostly played for laughs anyway).
Seychelles: Overlapping with Die for Our Ship like whoa. She's a Hot-BloodedPlucky Girl who has some Ship Tease and UST with both France and England in Gakuen Hetalia: obviously that makes her a total slutty whore who has no worth or depth as a character, is an offense to women everywhere, and must be horribly tortured and killed off.
Denmark: If there's a member of the Nordic Group that is likely to be portrayed as a total asshole in the fandom, it's Denmark. Sure, he can be pushy and Hot-Blooded and Norway sometimes hits him to keep him in line, but that doesn't mean that he raped and beat the Nordics into submission and that's why they don't seem to take him seriously. He could've easily treated Belarus badly in Hetaween, but he cheerfully accepted competing with her cosplay group — shouldn't that be a sign that he isn't evil or a Jerkass?
Everyone gets this by default in the popular Porn Without Plot setup in which defeating another nation in battle requires the victor to rape them. Apart from the many, many Squick and Fridge Horror problems with this, if this was true, Austria would have noticed Italy's anatomy much sooner. Not to mention it's very hard to sympathise with a victim when you know that the logic behind the setup would have required them to have done the exact same thing themselves; doesn't by any means make it okay, but it does mess with the impact somewhat.
The nations' attitudes to muggles in various fics might be an example of this, or not. The Gag Dub's dark humour does occasionally portray the nations as being remarkably flippant about mass murder and death; China criticises the others for not being totalitarian and seems far too happy when discussing his people's "crushing poverty", Russia offhandedly remarks that the USSR states came to live with him "after a little genocide, of course", and Germany threatens Italy with "ending up an experiment" and his response to Romano announcing a "surprise" is "Great. What is it, another Jew?" However, they never actually kill anyone onscreen, and it's debateable as to whether they're actually happy to do so. The dark jokes aren't present in the original, so this could be a case of the dub Death Eatering the sub.
You could argue that the nations had developed a dark sense of humor in the Gag Dub as a coping mechanism to living hundreds of years through various wars and crises, which commonly happens in real life for people who have to be surrounded by death and sickness on a near-daily basis (such as doctors).
One rather infamous example would be the Financial Crisis Gangbang, where someone on the Kink Meme requested a group of nations violently punishing America for causing another depression through his carelessness. The result was a fancomic in which America is somehow restrained by duct tape and horrifically raped and humiliated by England, France, both Italies, Germany, China, Japan, Prussia, and Russia. While all of those characters have, in canon, had times where they were pissed with America, the whole thing is way over what any of them have ever done (not to mention that in canon, their attitudes over the economy screw-up ranges from being obviously distressed to blaming America for being young and stupid to insulting him). A few follow-up fics have the offending nations suffer the same treatment, with them feeling entirely justified in what they did and wondering why America isn't simply walking off the trauma of being gangraped by his friends and family.
The doujinshi circle Hakka Pink is... a touchy subject in some parts of the USUK fandom due to their extremely unflattering portrayal of France. Yes, historically France did meddle in The American Revolution, but the Independence Sky series turn that "role" Up to Eleven via making France pretty much into America's slutty and psychotic Evil Mentor, ostensibly to make a Purity Stu-fied England suffer.
One of the biggest criticisms of the very polemic All He Ever Wanted is how it falls into this trope in regards to England, Japan, North Italy and specially Prussia, making the fic a very thinly-veiled Author Tract full of Writer on Board rants put in the characters' mouths and actions:
England: Tsundere former empire (canon) —> mentally-unstable Mad Oracle who supports the Axis and makes the world total shit because of it (AHEW verse)
The Russia/America fic "The Chosen End" is also pretty well known for subjecting England, of all nations, to this, all to favor Russia and America getting together. It's not helped by how the author wrote a fic where England is a crazy Yandere who tortures a wimpified, helpless America and sends him crying to Russia.
Fridge Logic tends to ensue with rapefics in Hetaliaverse when one wonders exactly how good an idea it would be to do something like that to someone who a) will live centures and is (going by the regular Unexplained Recovery and/or Good Thing You Can Heal scenes in canon) nearly impossible to kill, b) knows you are the above things as well, c) will have to work with you on a regular basis, and d) historical precedent shows won't be under your control forever. In cases of America being the victim, one also has to wonder how, since generally no explanation is given as to how a comparatively normal person manages to overpower someone who could swing adult buffalo around his head as an infant. China may fall under that heading too as he has been shown to be able to headbutt through a wall. As for Japan as the attacker, one may end up wondering why he'd go to so much effort when he thought merely being hugged was bad enough to ruin him for marriage.