Axis Powers Hetalia, despite being a show full of Ho Yay-fueled Moe Anthropomorphisms, has a fandom that's largely free of Ship-to-Ship Combat, probably because almost any pairing can be justified, and multishipping and Ship Mates are very common. But even it isn't completely free from this trope (...okay, the list below is rather long, but that's mainly because of Loads and Loads of Characters, and most examples are still limited to Vocal Minority status). In other words, even the nicest and most civil of fanbases - Hetalia shipping being on the whole wonderfully accommodating - can't eradicate the 'fanatic' in 'fandom.'
To simplify, the more popular the ship(s)/character(s), the more fanon will attempt to "kill off" the one that take the "spotlight" from their favorite pairing(s)/character(s).
England sometimes gets this from militant Russia/America fans who twist and warp his Tsundere behavior and possible crush toward America to Jerkass or even Yandere levels to make him into a pathetic Crazy JealousHopeless Suitor who can't accept that America doesn't want him or even a creepy pedophile who's been perving on America ever since he was a kid. The worst cases have England as a Domestic Abuser toward America who seems to have forgotten all about his own Super Strength or a Manipulative Bastard who uses poor America's undying love for him to emotionally abuse him. (Russia, if he appears, is sane and supportive to America.) Never mind that in canon, England has almost Woobie moments with America, or that America is actually a lot harder on him than the other way around. Or that Russia isn't the most innocent nation.
Pedophile!England perving on young America is not a rare phenomenon in stories that feature America with someone else and feel the need to justify the pairing by showing how horrible England/America would be... even though canon has zero evidence that would back this up; in fact, America seems to think back on their days together with nostalgia. Plus, if England has more-than-brotherly feelings for America, they seem to have been kickstarted when America was a teenager at the very least.
Actually Paedophile!England turns up an alarming number of times in colony central fics or to give a ex-colony a dark and tragic past for their lover to heal/save them from- never mind that in canon about the only person he's shown being regularly nice to is young America.
As for America, there are some fics that play up his stupidity and tactlessness to emphasize just how unsuitable a partner he would be for England. It is canon that America can be a jerk to England at times and is the main source of his heartbreak, but some rabid England/someone-other-than-America shippers(namely Japan, Australia and so on) would have you believe that America enjoys making England suffer and couldn't possibly ever be nice or flirtatious toward him without having some secret agenda to crush his heart again (while conveniently overlooking that America is canonly friends with England). This mentality crops up the most often in England/Canada fics, where it goes hand-in-hand with some Canada fans' bad habit of putting down America to make Canada look better too.
America also comes off badly in some Japan/someone-other-than-him fanworks where he's depicted as being in love with Japan instead of them just being best friends, with his somewhat tactless but genuinely cheerful and friendly attitude toward Japan in canon somehow being translated into him becoming unnervingly possessiveand stalkerish toward, if not outright abusing, Japan. About the only justification ever given for this is that America's dropping of two atomic bombs on Japan at the end of WWII must mean that he's actually a Yandere deep down, which completely ignores not only everything we've seen of them together in canon but everything else about their (currently good) real-life relations, so it can't even be passed off as "historical canon".
One of the most pervasive and venomous parts of this ship-related Austria bashing shows in the form of an infamous fanon that accuses Austria of having forced Hungary to put on dresses when she arrived to his mansion. There is no real evidence that he was the one who told Hungary to do so, and as far as we know it could've even been Hungary's own idea or even an order of her own bosses; however, lots of fans tend to immediately assume that Austria did so, and it's no surprise that many of them are either Austria/Hungary bashers who think he "reduces her to a Satellite Love Interest", or rabid Prussia/Hungary fans who accuse him of "keeping Hungary away from her True Love Prussia".
For Poland/Hungary fics, you can replace "Gilbert" with "Feliks" and it's the same. Apparently the Polish and Hungarian traditional friendship, their parts in the 1848 revolutions and the Austro-Hungarian Compromise that came in later equal to "Austria is cold and cruel and rapes Hungary every night and keeps her locked up while pretending they're Happily Married in public, so she whines and cries herself to sleep and needs to be rescued from her torture by a super manly Jerk Stu who only resembles Poland in name!"
Romania is starting to get this treatment from some rabid Prussia/Hungary fans, especially because many fans have liked him since his appearance and started shipping him with Hungary, even though Romania and Hungary are said to hate each other with a burning passion — which is easy to see as potential Interplay of Sex and Violence. He's also interpreted pretty badass due to the fact that he's apparently a mischievous yangire with a vampire vibe AND also uses Black Magic, which helped increase his popularity even more. He also looks like a combination between Hungary and Prussia.
While some Prussia/Hungary fans see Romania as a "serious obstacle" like they do to Austria, others treat the "rivalry" more as a Running Gag and make Prussia a prospect Butt Monkey whom Hungary is still Tsundere for, rather than a super Stu-fied romance hero who must "recover" his love interest from Romania's "dirty" paws and vampire teeth. And two/three others seem to favor an OT3 in which Hungary gets it on with both Prussia and Romania.
... And then this disappeared when Bulgaria showed up and turned out to be Romania's close friend and prospect Ho Yay partner.
Hungary herself, while normally embraced by fans for being an Action Girl and Yaoi Fangirl, isn't free of this. Some Germany/Austria fics portray her as a whiny, self-centered Clingy Jealous Girl or a brainless, weak, "girly"female who breaks the Austro-Hungarian compromise solely because Austria pays less attention to her than she wants to. Seems somebody hasn't read the Anschluss, New Year and/or Valentine strips, huh?
Russia in general has been used as a stock antagonist in many other shipping fics, not so much because the fanwriters hate him but more because he's the closest thing the series has to an "evil" character and they find it all too easy to crank up his "become one with me, da...?" line to a "you WILL become one with me, whether or not you like it, and only your true love can save you from my clutches, DA!" ultimatum. Suffice it to say that while he's no saint in canon, he's still far from the kidnapping, torturing, raping villain these kind of fics make him into.
Belarus, as the Yanderestalker of Russia, who not only is the fandom bicycle but also her brother, doesn't get nearly as much hate as you'd expect and many fans actually enjoy her Played for Laughs role as the stalker of the stalker. However, more serious fics that pair Russia up with someone other than Belarus often make her without a drop of sympathy or depth. True, Belarus canonically resents anyone Russia shows interest in and she doesn't get a Freudian Excuse or Hidden Depths regarding her behavior like her brother does, but the worst thing she did in canon was breaking Lithuania's fingers - and that was solely done for humor on a date that Lithuania himself asked Belarus for. Having her go out of her way to tie up and rape Lithuania just to prove the point of him being "unworthy" of Russia's love is probably taking it too far.
While it hasn't translated into outright Ron the Death Eater in fanworks yet (if only because most Turkey/Greece works simply leave Japan out entirely), the Vocal Minority of Turkey/Greece shippers can become very wanky toward Japan and the Greece/Japan ship when provoked, especially after the "provocation" of the anime faithfully adapting some of Japan's strips with Greece and Turkey that had been on the Web for years beforehand, with them deriding Japan as a Flat Character who only got the attention of Greece and Turkey because of him being a "gigantic Canon Sue who has half of the cast as his harem" and claiming that Greece loses all personality and historical depth when paired with him over his "far more interesting and historically important" rival Turkey.
Turkey has a case similar to France's (listed just below); he isn't demonized nearly as often by Greece/Japan shippers as you might expect as most of them view him as posing no real threat to their ship, but if they feel the need to have someone stir up some external drama for Greece and Japan, he's the one they're most likely to use. It doesn't help that exaggeration of Turkey's Boisterous Bruiser traits to Jerkass, Manipulative Bastard or Smug Snake levels is a not-uncommon sight even in non-shipping and Turkey-pairing fanworks, which can cause some fans to forget that Turkey is canonly friends with Japan and leans more toward being a Jerk with a Heart of Gold than an irredeemable Jerkass.
As for Greece, he's mostly free of this trope. Mostly. There are still some fans who are not pleased about him being paired up with Japan so often (and are not feeling charitable enough to simply make him Just Friends with Japan) and hence try to make him out to be a Jerk In Nice Guy's Clothing who lies about what "really" happened on that night with Japan or a pathetic Crazy Jealous Guy who exists solely to bitch about how Japan's not with him and thus come off as worse than the nation the author wants Japan to be with instead. A few of these fans even claim that Greece hangs out with Japan only because he wants to get into Japan's pants, even though a read-through of all his strips with Japan will show that this is almost certainly not the case. It's pretty mild compared to many other characters' cases on this list, but it still really stands out in Greece's case, considering his sleepy Kindhearted Cat Lover personality in canon.
A more subtle yet venomous and insidious way to make France look bad in USUK fics (principally doujinshi) is to take the French Crown's historical role in The American Revolution and flanderize it by characterising France as a borderline Evil Mentor to America who sleeps around in the war camps and seems to have fun by pitting a young and easy to manipulate America against his eternal enemy England under the excuse of "giving America the chance to develop into his own country", but actually just wants to make England suffer and get revenge against him. Way to twist ~historical canon~ to fit your ship preferences, people. To be fair, one of the main reasons that the French Crown got involved with the American Revolution was to get revenge on England for the Seven Years War. In canon, France is pretty self-centered and likes to cash in on other people's victories, so him being a "borderline Evil Mentor" isn't that out of character. But it can (and more often than not, is) taken too far, with France as spiteful and pit against a Purity Stufied England.
Believe it or not, North Italy gets bashed by rabid fans who'd rather pair up Germany with others, especially Austria or Germany's older brother Prussia. Some shippers of Germany/Prussia are notorious for turning Italy into a Psychopathic Manchild who actively sexually, emotionally, and physically abuses Germany, so that Prussia can come in and rescue his younger brother and offer him a "truly loving" relationship.
North Italy's big brother Romano has lately been getting this piled on him too, by those who can't stand his abrasive personality and would prefer Spain be with a more "suitable" (or "historically important") partner like France or Netherlands. It's often forgotten that both Romano and Spain have issues with their personalities and in dealing with each other and that South Italy has shown more than once that he genuinely cares for Spain underneath it all (the major proof comes when when Spain falls sick and Romano goes searching for a cure, willing to deal even with The Mafia to help him). All this hasn't stopped the detractors from derailing South Italy into a horrible boyfriend that you wonder how Spain could ever have been cheerful around, or making Spain into the worst case of a Love Martyr who must be saved by France. Unless we talk about him actually raping and torturing North Italy to "keep him in check" and "away from the potato bastard" (re: Germany).
In the rare Romano/Belgium ships they occasionally seem to change Spain from a good-natured, happy character who cares about Romano's wellbeing into a perverted caretaker. That being said, they do have an equal chance of making him have an I Want My Beloved to Be Happy moment, which is less of a character derailment that the former.
There are also cases of Prussia/Romano shippers twisting canon in fic and comments to paint Spain as a pedophile and perverted moron that willfully neglects poor Romano's needs, making Romano out to be the Love Martyr in this case and making Prussia out to be the savior who must free him and give him a truly loving relationship.
There are a distressing number of stories where America, North Italy and/or Poland's natural ditziness illustrates how they'd be unsuitable partners to another character (often England, Germany or Lithuania, respectively). Yes, America's not the sharpest knife in the drawer, but he's not a moron that needs help counting to ten; Italy may not take everything seriously, but he's not brainless; and Poland is flighty, but he's most certainly not an idiot that makes a chimp look like Einstein in comparison.
While still rare (we hope), some rabid Prussia/Canada fans are really horrible not only to France, but to Cuba too. Because not being a Bishōnen and mistaking Canada for America apparently makes Cuba a horrible bully whom Prussia must defeat to release poor uke Canada from his abuse, obviously missing how Cuba is very apologetic whenever that happens and how they get along extremely well otherwise.
Though extremely rare, Sweden gets this treatment from time to time in Estonia/Finland fics; usually becoming an abusive "husband" keeping Finland from Estonia, or something of a Stalker with a Crush that poor little Finland is too weak to push away.
Some fanworks take Denmark's canon Boisterous Bruiser traits and make him an insane Yandere who drove Sweden to run away with Finland after raping and torturing him into almost insanity. Even some works that are ostensively Denmark/Sweden use this; there's a very popular doujin that represents the infamous Stockholm Massacre by first making Denmark severely injure Sweden's eyes with his axe when Sweden merely says something that sounds like he'll leave the Nordic group (which "explains" why Sweden uses glasses), and then torturing and raping him among the ruins of Stockholm right after his defeat.(Though that doujin a;so has a rather cute reconciliation between the two them at the end.)
...with the exception of Japan who was getting just as bad Relationship Sue accusations from the Vocal Minority of W-fen long before the above cases came to light, with them making his LOATS status in J-fen out to be a horribleMisplaced Nationalism crime worthy of bashing him for alone. Some of them even used this to discredit the England/Japan pairing (many England/Japan fics do suffer from OOCness and Relationship Suedom for Japan, but that doesn't mean that the pairing itself has zero credibility!). And when they found out about the Greece/Japan/Turkey triangle, their accusations got truly ridiculous. All while the majority either ignored them, squeed over the episodes, or went "...What, you're just learning about Japan's relations with Greece now? Boy, you really need to read the webcomic in full."
The biggest female victim is Seychelles, the local Nubile Savage and Plucky Girl. She was a minor character with a mere cameo in the comics... then she became an Ascended Extra in Gakuen Hetalia (both the original script and the PSP game), and then the poor girl started getting shit from everyone coming from everywhere. The Het is Ew camp called her a Relationship Sue and the USUK and FRUK rabidshippers accused her of being a slut and standing in between their beaus because she had some degree of Ship Tease with both England and France. (Nevermind that France is after Anything That Moves, that Gakuen Hetalia isn't that centered in romance but more in The Power of Friendship, and that in the PSP game itself Seychelles actually helps America to regain England's attention and affections after a fight, which can easily be interpreted as her Playing Cyrano for them.)
Belgium may not be as big of a target as Seychelles, but she still gets potshots from rabid Spain/Romano fangirls that falsely accuse her of standing in between. An apparently Lost Forever Spamano fanart has Canada threatening to hit her (yes, CANADA) because she won't give up on interferring with them, and we're supposed to cheer for Canada when he says he'll hit her.
Even Vietnam, who has had barely any screentime at all gets this from people who dislike how some members of the fandom pair her up with America, Russia, France, and/or China and refer to her as a Relationship Sue because of Fanon portrayals. Despite the fact that, in canon, she has not had any Ship Tease with anyone other than Taiwan and Thailand so far, she has gotten some accusations of being a Flat Character who only exists to ruin other pairings. Thankfully, this portion of the fanbase is very small in comparison with hate that the other females have gotten, as it's very easy to ignore her character entirely.
Lithuania tends to get accusations of being a Marty Stu from fans who pair Russia or Poland (or America or Belarus...) with someone else. Not all of it is because of this; Lithuania is, after all, portrayed as a verysympatheticNice Guy for a country that was once powerful, and Himaruya seemed quite fond of him in 2007-2008 (though this has improved since, with him being passive-aggressive and rude towards Prussia in a recent sketch). But a few fans have admitted to disliking him just for "getting in the way" of their ship.