Pretty much the only way in animation to make someone ugly or unusual looking is to do it deliberately and without subtlety. If a character is not attractive looking, they're usually absurdly ugly. The result can be extremely jarring if it deviates too much from the rest of the show's look, although it tends to be more tolerated in comedies and non-human characters.
This is because of Generic Cuteness. Occasionally, Artistic Age means that Gonk has to be applied to make older characters seem downright decrepit in order to seem older than the generically young cast. Compare No Cartoon Fish and Nonstandard Character Design.
Of course, beauty is in the eye of the beholder, and some Gonks may be viewed as rather cute to certain viewers.
Please note: While it is possible for characters to be "Gonk-ified" at some point, it's usually only temporary. Real Gonks look ugly by default.
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Anime and Manga
Most fat characters in anime suffer from some level of Gonk. Examples include:
Though just as often regarded as physical pinnacles, Sumo wrestlers are occasionally referenced in anime as being gonk.
Leiji Matsumoto characters come in two flavors: catalogue model and gonk. Notably examples of the latter include Captain Harlock's sidekick Tochiro (and his seemingly endless line of identical ancestors. How a family line with men that ugly manages to continue one for so many millenia is the greatest mystery of the Leijiverse) as well as most of the other men on the captain's crew of Jolly Space Pirates (Harlock makes a point of not recruiting anybody handsomer than he is, since he also has several beautiful women on the ship). Most incarnations of 999's Tetsuro are also very gonkish, though he was considerably bishified in The Movie. Also, the entire population of Earth, sans cyborgs, during the Big Fat Future of the manga's second story arc.
Blue Drop has Hiroko, the leader of the high school dorms. She may not be straight-on gonk in and of itself, but she's so ridiculously large that she skirts the line.
Okada from Alive: The Final Evolution, the only power-user who is overweight. He sweats constantly, may have a subtle hentai (hand-drawn porn) fetish, and suffers from an inferiority complex due to his physical appearance. His power involves killing victims who break their "promises" (for ex. two guys are killed when they call him fat despite being promised not to say so). Don't forget Han and ratty scientist Kairu. Oh, I can't forget Kurumi, crazy stalker girl. (She becomes much prettier after losing weight later.)
BECK has at least a couple. Koyuki's friend Tanabe appears to be fourteen going on forty at the start of the series, and the gentleman who sells him his Fender also has some physical oddities.
Several of the less important shinigami characters in Bleach - but most of the shinigami outside the main cast are just comic relief/cannon fodder, so this is understandable.
Ganju is known specifically in the story for being ugly, and many viewers may agree he is either a Gonk or borderline Gonk. But this is by Bishōnen standards, where Hollywood Homely may be ugly. To Bara Genre standards, Ganju's rough worn guyish looks actually make him look hot.
Most of the thugs and gangs in the backgrounds of the Karakura Town scenes.
Charlotte Chuhlhourne is this.
It's a blip, but one episode of Cromartie High School took place in what was basically a gender-flipped version of the main (male) characters' high school. The "girls" in the school were very much as if the delinquents were crossdressing... poorly. Moustaches and all!
Desert Punk has quite a few. If a character is unnamed or over 40, chances are they're gonks. The titular character is pretty normal looking but becomes gonked out if he's doing something disturbing.
Sumiyoshi from Excel♥Saga. One episode has his gonkness drained out of him, turning him into a generic Bishōnen. His friends are visibly shocked, and he doesn't seem to be pleased with the change either. It was eventually shown that he gets it from his mother.
The Puchuus in the Excel♥Saga anime are cute mascot characters whose faces become Gonk (resembling scarred, haggard manga assassin Golgo13) when they are injured or killed.
In Ga-Rei, anyone who isn't a main character or relatively young is ugly. It's a bit jarring to see the really attractive Kagura next to the extremely old-looking Fujiko, for example.
Getter Robo teams always have "The fat guy", with varying levels of gonk. Musashi from the original looks a bit gonkish, especially compared to his impossibly handsome teammates (and his ridiculous, slapped together "uniform" doesn't help, either), but most of the subsequent incarnations had Musashi or his equivalent drawn with the similar rugged good looks to his compatriots. Kaede from the all girl Getter Robo Zan team is probably the gonkiest of all the Getter pilots (being a Distaff Counterpart of Musashi), but then again all the girls on that team are pretty homely by anime standards.
When you compare the likes of Musashi, Benkei, and Gai to the worst this trope has to offer I think it's a little harsh to call them outright gonky just because they're big.
Far, FAR more gonkish are "Build Angels" Mido and Monko of Kotetsushin Jeeg. Mido is tall and slender to a creepy degree, while Monko might have been able to pass for a bodybuilder-style Amazonian Beauty if she didn't look like she had a man's face pasted onto her body.
An unusual example in a serious anime is the sinister Kazundo Gohda (or Gouda) from GitS: 2nd Gig, whose face was hideously disfigured in an accident. Gohda decided not to have his face reconstructed because his new appearance made him distinctive and nobody who meets him will ever forget him. This is deliberately contrasted with Hideo Kuze, the show's nominal (but less villainous) villain, whose prosthetic body wears a handsome mask-like face.
The Home Affairs Minister, on the other hand, is the conventional sort.
Kare Kano featured a flashback of a guy who had considerably improved his appearance since he was a child. He's drawn in a completely different style than everyone and vaguely resembles a Fisher Price toy.
Kemeko from Kemeko Deluxe!. Short, ugly and yet thrown into more outfits and situations than a character of this type should be in.
Curiously, when seen early on in some sort of maintenance bath, Kemeko appears to be patently feminine, only to revert the instant it's cleaning cycle is finished.
Deconstructed on three separate occasions in MÄR, all of them by villains from the Chess Pieces.
The first gonk, Rapunzel, is an extremely ugly, hag-like 29-year-old whose sensitivity about her appearance has turned her into a violent, murderous, backstabbing psychopath who enjoys killing everything that's "ugly" to her, especially women.
The second gonk, Emokiss, is equally sensitive, though unlike the previous example her ugliness is self-inflicted, as she's constantly seen eating. She actually destroys her sentient Guardian �RM after it comments on her ugliness.
The third gonk, Kouga, is not NEARLY as sensitive as the previous two; his problem is that, because of his ugly face, he has become delusional that ugliness equals goodness. Because of this, naturally, he is the only one of the three gonks in MÄR whose sheer disgust for beautiful people is actually genuine, and NOT from denial.
Ryu from Mobile Suit Gundam is a bit of a borderline case, as he's usually drawn in a slightly different style than most of the main characters, but he's not really ugly (in fact, in the novels Sayla has a bit of a crush on him before she ends up getting together with Amuro).
Justified in Naru Taru with Sato's fiancee, whose odd appearance is due to Down's Syndrome.
The world of One Piece is not only a World of Ham, but a World Of Gonk living in harmony with a World of Stunning. So many characters, ranging from protagonists, antagonists, and even neutral background characters, are incredibly out there and ugly, yet go hardly unnoticed because it just happens all the time. Worth noting that the Grand Line has more gonk than the rest of the ocean; whether this is due to Oda's art evolving to be more free or the Grand Line actually being just that weird... we're not too sure.
Alvida, setting the standard as the first villain we see. Then she eats the Smooth Smooth Devil Fruit between story arcs and becomes incredibly slippery... and slender, and stunning. And everyone's object of lust.
Wanze and Duval. So Gonky that repeated kicks to the face rendered them better looking. Duval happens to look exactly like the poorly drawn wanted poster of Sanji, which in and of itself is Gonky in how it exaggerates Sanji's attributes, especially his spiral eyebrow.
Emporio Ivankov, a transvestite based on Dr. Frank-N-Furter, has quite an odd facial expression with a face locked into an almost perpetual grin and eyes wide open. Mr. 2 also has quite an odd face for being a crossdresser, enough so that when he decided to make the world's weirdest face from a collection of all the faces he's encountered, he only had to add Usopp's nose in place of his own. Both of these characters come from Oda's appreciation for transvestite culture, expressed in an odd way.
Most of the members of the Blackbeard Pirates are gonks, such as the titular Captain (Luffy's evil counterpart) and most of the new members. This may go with the crew perception of being Psycho Rangers to the Straw Hats.
Big Mom is a particularly terrifying example, being incredibly huge with bulging eyes, a large nose, and a permanent grin. Doesn't help that she eats her own crew mates and destroys islands under her protection that don't pay her back in candy.
A strange example occurs in Ouran High School Host Club when the host club does this in an attempt to cheer up Haruhi. Since the show already has quite a few crossdressers, they (with the exception of Kyouya, natually) end up in hilariously overdone makeup to make the situation funny.
Pani Poni Dash! has several, most notably Yankee, whose picture is at the top, and the hordes of identical Itou-sans. Then there's the characters who are drawn to look very similar to their real life originals, which...doesn't quite mesh with the Puni Plush cuteness of the rest...the Tommy Lee Jones Circa Men In Black for example is especially jarring, as he's mostly seen with Ichijou...who often sports an even simpler face than normal.
Konatsu's step-family in Ranma ˝ is deliberately made hideous, despite them being hostesses at the "Sexy Kunoichi Tea Spot" (a brothel, the reader is made to assume, or at least an extremely exclusive parlor.) His stepsisters are either gangly and monkey-like, or gigantic and with lips so huge they are her entire face. To say nothing of the shrunken, yakuza-faced step-mother. This makes Konatsu by far the most attractive woman, even though he's a guy.
Another exception, Sailor Moon has one of Usagi's schoolfriends who pops up now and then in the first few episodes of the show. She's chubby, but not ugly in any way. She gets Brother Chucked pretty fast along with the rest of Usagi's former friends after other Senshi start showing up and she hangs out with them instead. Sadly, while the other girls had names, this character never did (and this is a show that has been known to give names to the most minor of characters in the guidebooks) so fans can only identify her as "Usagi's Fat Friend".
Some of the episodic Youma/Daimon/Whatevers are pretty damn gonky too, with the final season, as serious as it's supposed to be, having a ludicrously high ratio in comparison to arcs where that would be more fitting, say the Dark Circus arc. (The completely ridiculous looking 'sailor parody' enemies)
Actually averted in the film Spirited Away. Miyazaki didn't want his female protagonist Chihiro to be overly beautiful, in order to reinforce her presentation as an average girl at the film's beginning. He managed to succeed at this task without having her look exceptionally ugly or out of place, capturing just the look he was going for.
Yubaba, the witch that runs the bath-house, is Gonk. And, obviously, her twin sister, Zeniba, would be as well.
Kimo-o in the manga Stripe Blue. He's totally unaware of how freaking creepy he looks, and the fact that he also acts like a lunatic doesn't help.
In Team Medical Dragon, it's possible to identify the good and bad guys by one characteristic alone: most of the time, the good guys are drawn incredibly attractively, while evil characters invariably look like the products of 18 generations of inbreeding.
The villains sure are ugly (as hell), but the sympathetic male characters range from heroically handsome over small and dorky to The Big Guy. The women, of course, are attractive. The patients look sickly.
Tenchi's classmate Kazuhiko Amagasaki in Tenchi Muyo! is an iconic one, to the point he actually had a short-lived subtrope inspired by him ("The Fat Guy with Big Lips and Pimply Nose"). He appears mostly in Tenchi in Tokyo.
Leeron may count too, the guy may aim to be a Bishounen, but he still looks like a frog.
Jougan and Balinbou aren't exactly pretty either.
Another exception — In one episode of Tenjou Tenge, we learn where female villain Emi Isuzu keeps all her hidden knives: she's really quite obese, and uses ki techniques to compress her fat and use it to carry concealed weapons. However, her full-sized form is completely Gonk-free, though it doesn't stop Maya (who learns Emi's big secret) from teasing her about it.
Whether or not it's Gonk-free is really arguable; this editor found it laughably Gonky.
A lot of the lesser villains in Yu-Gi-Oh!. While Ushio and Kai look rather decent, the others like Kujirada and Nezumi (whose name means 'rat' in Japanese), are outright gonk!
The Seto Kaiba imposter (posing as his ghost) in the Duelist Kingdom arc is horrendously this once he drops the charade.
Generally speaking all of the villains of the week from the first seven volumes were ugly, perhaps to emphasise the ugly side of their personalities. Dark Yugi also noticeably had the same eye shape as many of these characters, although he was never outright ugly.
Yu-Gi-Oh DM's spinoff series, Yu-Gi-Oh! GX also deserves a mention. Following in the footsteps of its predecessor, GX has numerous Gonky characters (mostly villains), the most notable of which being Professor Chronos de Medici (Vellian Crowler) and V.P. Napoleon (Jean-Louis Bonaparte). Jun Manjoume's spirit partners, the Ojamas, also qualify. To be fair, though, the series makes up for all the Gonk with an entire gang of cute/Bishounen heroes.
Kimura from Azumanga Daioh, with his perpetually gaunt and slack-jawed expression.
Samurai Champloo utterly subverts this, being able to have attractive and unattractive characters from one end of the spectrum to the other and in between without any stylistic major shifts.
In one episode, Fuu is forced to work off her debt in a brothel. While "on display," she deliberately contorts her face into Gonk Mode to discourage customers from choosing her. Unfortunately, that face happens to catch the eye of another Gonk...
Many of the youkai in Natsume Yuujinchou look this way. Nyanko-sensei in particular, has come to be known by Natsume's friends as "Natsume's really ugly cat" - if they don't mistake him for a pig, that is.
This is accurate, though: the vast majority of yokai are described in folklore as really bizarre-looking.
Doronjo's sidekicks Boyacky and Tonzura from Yatterman fit this. In fact, they're so ugly they actually look cute.
One of the more prominent running gags in Kenichi: The Mightiest Disciple involves Ragnarok member Loki having numerous body doubles a la Saddam. One of the body doubles is moderately gonky and looks extremely out of place when compared to the rest. Come to think of it, he◊ bears a passing resemblence to Henchman 21.
Kemonozume has a number of these, most obviously the main villain, Ooba Kyuutarou.
Arguably, 8th from Mirai Nikki. She's meant to look more like a cute chibi than outwardly grotesque, but her appearance compared to the other characters can be quite jarring.
In Rurouni Kenshin most minor villains, especially those belonging to gangs, are Gonks.
A group among Shishio's followers, the Priests of Abukuma, are particularly notable. Each one of the four have the most comically hideous faces, and the first thing they even talk about is sex!
And in Samurai X, we have Iizuka, Kenshin's 'handler', drawn noticeably less attractive than the rest of the male cast likely because of his propensity for betrayal.
The linemen Kurita and Komosubi of Eyeshield 21 are both pretty gonk, though in an Ugly Cute sort of way. In contrast to most examples, they are part of the main cast and are every bit as important and well-developed as their more attractive team members.
Kasamatsu of the Taiyo Sphinx. He's about as tall as the average character in the series, but he's about three times as wide, with a really exaggerated face. He really, REALLY stands out among the other two important members on his team, the bishounen Harao, and the adult-looking Banba.
The entire Sankaku Punks. All of them. Even their coach has a triangular shaped head.
And the announcer, too, has hair that spins like a windmill when he gets excited. Which is all the time.
In Fairy Tail, there's Virgo's initial appearance under the ownership of Everlue. This is because Virgo is so loyal to whoever her master is that she actually changes her looks to whatever pleases them most. Under Lucy's ownership, she's one of the prettiest characters in the series.
Many, many characters in Shiki due to the insane art style, but Masao is especially Gonk... and has the personality to match.
Done in a very literal way in the Bludgeoning Angel Dokurochan anime when one of Sakura's classmates is turned into a monkey. His face and head are animated in a paper cutout style, in a completely different form of animation from the rest of the show.
Let us not forget about the angels with their halos removed. Extreme case of explosive diarrhea happens. Poor bastards.
Inko-chan from Toradora! is a pet parrot Gonk, of all things.
In the infamous "Sandbox Sequence" from the complementary conclusion to Neon Genesis Evangelion, The End Of Evangelion, Shinji sees two doll-like girls with very disturbingly-accentuated features, that definitely fall under Gonk. As with Perfect Blue (see above), it is NOT played for laughs.
Andre from Kangoku Gakuen, who definitely stands out the most considering how normal looking everyone else is. He's large, has an egg shaped body, a face that is way too small for the rest of his head, and over-sized Budha-like earlobes.
In Nanatsu No Taizai, as a contrast to King's normal child-like fairy form, his human form is a fat slob-looking man
Many of the titular Titans from Attack on Titan. They are generally designed to look like misshapen mockeries of human beings with ridiculously goofy facial expressions. This doesn't make them any less terrifying in-universe. The ones shown that don't qualify for this trope (the Colossal Titan, the Armored Titan, Eren and the Female Titan) are even more dangerous.
Dick Tracy used this in many of its villains, such as Pruneface, Flattop, The Brow, Rodent...
A lot of good guys in the strip too, like the smelly hillbilly B.O. Plenty and his hag-like wife Gravel Gertie.
The Yellow Bastard from Sin City stands out, but Marv could possibly be viewed as this as well, due to the impossible skeletal structure of his face, but in his case, it makes him look equal parts gonk and equal parts badass. The same can't be said for That Yellow Bastard. He's just one ugly (and smelly) dude.
Nothing "possible" about it. It's stated in "The Hard Goodbye" that he's so ugly even the prostitutes won't touch him. Goldie was the one exception, and when she gets murdered he spends the entire rest of the story on a Roaring Rampage of Revenge against her killers.
Penelope Platypus from Sonic the Hedgehog looks more or less like a cartoony platypus on two legs wearing a backpack, while other orginal females from the comic have the figures of developed young women, yet still retain animal heads and fur.
A lot of Archie's supporting characters in the early decades qualified. In the '40s, most anyone outside the main cast fell under this trope; Miss Grundy was almost toothless and had a prominent wart. Well into the '80s, being a Gonk was Big Ethel's defining character trait. Both characters have had makeovers in the last couple of decades; Miss Grundy has upgraded to Cool Old Lady status, and Ethel is tall, lanky and a little mannish, but no longer a runner-up in the Lena the Hyena contest.
One classic example of a particularly ugly Gonk is "Sloth" of The Goonies fame. His Gonk-ness was actually so striking, his initial appearance was enough to shock and initially terrify one of the protagonists, "Chunk", before he was later revealed to be a Gentle Giant.
In What Planet Are You From?, Garry Shandling played a Gonk. It counts as character design because the problem wasn't his natural features so much as his 'I just ate a bag of lemons' expression. By the end of the movie I had to turn away every time he came on. (He was the main character, so that was a lot.)
That's not too far off from Shandling's normal face, really. While calling him a real-life Gonk would just be mean, he's still never exactly been a heartbreaker.
Hongkong slapstick comedies will sometimes cast such ugly actors just to get this effect.
Not to be insulting, but Danny Trejo is typically cast in frightening roles precisely because his unusual features make him look intimidating. Peter Lorre would be an earlier example, with an appearance that made him easy to accept as a villain. Maybe has Unfortunate Implications for all of us. Ditto the character actor Brion James.
In Ralph Bakshi's The Lord of the Rings most of the hobbits are fairly normal looking and the younger ones look like children, but Samwise is very ugly. He has a huge head, crooked teeth, a big nose and chin, and at times seems to have a lazy eye.
The other hobbits are aristocrats, or what passes for it in the Shire: Merry is the son of the Master of Buckland (Saradoc Brandybuck), Pippin is the son of the Thain of the Shire (Peregrin Took), and Frodo is from a wealthy family closely related to both the Brandybucks and the Tooks. Sam is, basically, the son of Frodo's groundskeeper. So commoners are ugly.
Mok Swagger from Rock and Rule. Despite the entire cast consisting of anthropomorphic furries, most look human, while Mok looks severely deformed, or like a plastic surgery experiment gone wrong.
Corporal Nobby Nobbs from Discworld is ugly enough to require documented evidence to prove that he's (probably) human, and to completely avert and/or subvert the Attractive Bent-Gender trope (this is footnoted in the text itself). Official art of him fits the trope.
Ichabod Crane, the protagonist of The Legend of Sleepy Hollow, is described as rather odd-looking, having a small head, big ears, a long nose, long arms and legs, and a very skinny build. The narrator even compares him to a scarecrow and a grasshopper.
Match Game: Several questions over the years have featured characters who were super ugly, asking the contestant to fill in the blank with something to compare the subject's ugliness to. Usally, the punch line is a movie monster, such as King Kong or Frankenstein.
Sanford and Son: Fred's cruel jokes about Aunt Esther have included remarks about her being as grotesque in appearance as King Kong and Godzilla, among other movie monsters.
Father Jack from Father Ted is incredibly ugly, with stringy unwashed hair, crusted lips and skin, and a near-permanent grimacing snarl. Word of God says that Frank Kelly always had to eat alone when on set because the make-up that was used to transform him into Father Jack was disgusting enough to put the rest of the cast and crew off their meals.
Half of the non-Puppet aliens in Farscape. They seem to try to go overboard on crusty features and grotesque prosthetics. Good examples are the "Tavloids" (Tavleks) in the Season 1 episode "Throne for a Loss", with their oversized mouths and metal-dome heads; and especially the "Plakavoids" (Plokavians) in Season 2's "The Ugly Truth", whose faces appear to be melting off their skulls.
The Breaker (manhwa) generally avoids this, except in the case of Mamungi. The protagonist calls him an ork, but his badass master just calls him frog-faced.
Cathy bears the unusual distinction of having a Gonk protagonist, with gigantic eyes, stringy hair, and no nose. Out-of-universe, she's sometimes considered Ugly Cute, but in-universe she remarks that the only people who've ever called her attractive have been trying to sell her things.
Given the general drawing style of that strip, she's really more Hollywood Homely (in that none of the other characters are drawn in such a way as to appear much more attractive), and she's certainly not Lena The Hyena.
Ape Escape: Monkey Yellow is a good example of this. And he (she?) considers himself (herself?) the best-looking character in the series.
Eunice in Bully. Subverted in Beatrice, who would be attractive if she lost the glasses and got some Abreva for her mouth.
The EarthBound (or Mother) series has a few Gonks, primarily in their fat female characters; however, Lardna Minch is their queen. Maybe it's something about how her mouth is bigger than the rest of her head, or how plastic and grotesque her smile is, but it's kind of disturbing.
And her son Pokey looks quite disturbing, even for someone of his weight; when he fights alongside Giygas in the final battle, he appears to have blue skin.
A part of it is the fact that his hair obscures his eyes and his mouth is always open. His 3D models in Brawl are even creepier.
Queen Brahne in Final Fantasy IX, who outranks most of the monsters in the game in sheer ugliness for no easily explained reason. This may be a vague dig at Beauty Equals Goodness (compared to the villainous but attractive Kuja) as her subjects usually insist Brahne is a competent and respectable leader, at least pre-game. It is particularly bizarre because her daughter doesn't look anything like her which theoretically isn't a problem because Garnet is revealed to not be her biological child. Except that Garnet was adopted by the royal family because she looked close enough to the real Princess Garnet to take her place, which means that Brahne still had a biological child that looked nothing like her.
On a similar note, a good proportion of Final Fantasy characters for the first six games in the series are Gonks, due to the fact that main artist Yoshitaka Amano has no middle ground between "is that even human" and "TAKE ME, YOU GORGEOUS DEVIL, TAKE ME".
Every Fire Emblem game includes one playable gonk (except for Fire Emblem Awakening, though Oliver is playable as a semi-secret character via StreetPass). The bandit class seems to be solely composed of these. In fact, one can pretty reliably tell which enemy characters will eventually join the player... they're the ones who don't look like either a monkey's behind or Morticia Addams.
Gannon the carpenter from Harvest Moon DS: Island of Happiness is considerably less attractive than the other inhabitants of the island. His daughter Eliza, on the other hand, is so cute it hurts.
The Gourmet. Dear lord, the Gourmet. Some fans are convinced he's not actually human. Island of Happiness and related replaced him with a cute kid Expy.
Most of the characters in the Kunio-kun games are generically cute... except for Misuzu, who is a seven-foot schoolgirl with a head the size of a pumpkin and the face of a middle-aged woman.
The infamous CDI Legend of Zelda games had characters whose ugliness was matched only by their sheer awful voice acting. The main characters are drawn heavily off-model. Everyone else is downright grotesque.
Gutsman's operator Dex in the Mega Man Battle Network franchise. Naturally, his Star ForceExpy Bud also falls under this. Dex looks like some strange obese shark person, while Bud is some obese guy with his hair shaped into horns.
This might be a possible shout out to Astro Boy 's designs; Osamu Tezuka characters have a distinctive old-school flavor that often looks really strange to newer anime fans.
A non-fat gonk in Persona 4 would be the homeroom teacher, Kinshiro Morooka, aka "King Moron," who seriously needs a dentist. Possibly a dentist with a hacksaw. He also bears a striking resemblance to Steve Buscemi, which just makes things worse.
And then there's Mitsuo's fish-eyed face making him look for all the world like the Gerber Baby, but in his case he's supposed to be unsettling for a different reason.
For the less-subtle variety of Gonk, Persona 4 also has Hanako, a fat female student who's in cahoots with a female homeroom teacher who also shares herdelusion of being irresistable to the other sex and later enters a beauty pageant with her.
Robopon has Gonks in quite a few Robopons' evolutions, particularly in the first game—Uggy is one example. Even more jarring if they evolved from something cute.
Gen-An Shiranui from Samurai Shodown is so terrifically ugly that it is impossible to even tell his species. (He's not a tengu, and he's not an oni, but he definitely isn't human...)
He's a follower of the dark back, and in the second game he's a zombie.
There's also obese Texan ninja Earthquake, and then there's Kusaregedou, who's uglier than Gen-An and Earthquake combined.
Rufus from Street Fighter IV, although as a martial artist, he's definitely in-shape. (Spherical is a shape, right?)
Yohm from Breath of Fire IV is pretty much the prototypical example of Geezer Gonk. Stick legs, round body, his nose looks like a potato, and the impression one gets is of Anpan Man gone terribly wrong and evil.
Roughly one-third of the characters from Infinite Space can be considered as Gonks.
The Ace Attorney games have otherwise normal to attractive characters have gonk moments, but special mention must go to eternally gonk Sal Manella, the sweaty otaku TV director, and perverted hospital "director" Hotti.
Mike Meekins, the clumsy officer with a No Indoor Voice may not as be as ugly as Sal Manella or Hotti, but he's incredibly gonkish when compared to his fellow workers with his beady eyes and ridiculously big chin.
Super Mario Bros.: With their huge pink noses, constantly clenched teeth, wicked mustaches and nonstandard bodily proportions, Wario and Waluigi are a lot uglier than the rest of the cast. However, that's part of their charm.
Although many NPCs in The Elder Scrolls IV: Oblivion are homely at best and hideous at worst due to the random face generation, there are a few that go to cartoonish extremes. One member of the Leyawiin Mages' Guild who turns out to be evil has a ridiculously large forehead for no apparent reason. Also, pretty much everyone in Hackdirt, but especially the "Breathren", although they have the excuse that it's implied they're descended from nonhumans.
Stunfisk in Pokémon Black and White. It's not so bad (Okay, yes it is), but it lives in a world of cuteness. Ironicaly, in the Pokémon anime, Cilan, a character known for his good looks and Bishonen-ness, is the one who catches it.
Jynx is a Gonk all the way from the Indigo League. It also looks like a blackface caricature, possibly intentional assuming it's a combination of Black Pete and an Opera Singer. Another interpretation is that it was based on Japanese fashion trend "Ganguro" but Gamefreak admit they don't remember what they were thinking when they drew it, most likely it was this trope.
Binacle from Pokémon X and Y. Two barnacles attached to a rock, each with a rather squashed, nonstandard design for a face. Some people have jokingly compared it to The Ugly Barnacle.
Jet Set Radio has a collection of colorful and unique-looking characters. Soda◊ takes this a step further with his tall height, long limbs, big nose, and odd hairstyle, which make him look sorta like a Muppet.
Waluigi in Brawl in the Family is particularly hideous among a cast of generally-adorable characters.
Reika Kongouji, from Getter Love!! And she's female!
On his first appearances, William Winsbury in Gunnerkrigg Court is markedly uglier than the main characters, with his odd colouring and pointy teeth. After some Art Shifts, and as he becomes a less unsympathetic character, he gets rather more handsome.
Ménage ŕ 3 has a very pretty lead and secondary cast (of both sexes), one or two Hollywood Homely supporting characters — and Eulice, the downright simian landlady. (Though even she claims that she used to look like sex goddess DiDi.)
Turns up now and again in Ow, my sanity. Once lampshaded (most likely by coincidence) by having Nancy actually get squicked enough into feeling fear.
Equius in Homestuck wears a pair of shades with cracked lenses to hide some really huge bags under his eyes, has stringy hair, a set of broken teeth and tends to sweat a lot.
Gorgeous Gal, a huge elderly featherless bird who wore a green dress, lots of jewelry and a white wig is supposed to be this in the Woody Woodpecker short 'A Fine Feathered Frenzy.' When Woody sees her for the first time he turns white as a ghost and passes out. She even breaks a hand mirror by batting her eyelashes at it. Gorgeous Gal's face is actually rather cute like most cartoons of that era. She also flirts with the woodpecker with a sexy voice so not all members of the audience who view this cartoon find her completely unattractive. Woody however is not interested but she is much older than he is. Also compared to Gorgeous Gal he's about the size of a puppy. Gorgeous was still smitten and enjoyed lifting him up and pressing her giant red lips against his much to the woodpecker's dismay. She also marries him and makes love to him off camera despite the woodpecker's feelings.
The American film Quest for Camelot utilizes this with its villain, Lord Ruber. His huge misshapen body and shrunken face makes him really stand out from the other Knights of the Round who are perfectly normal looking people. Presumably this is so you can tell he's the villain, but this begs the question of why some freaky guy like this was ever let onto the Knights of the Round in the first place.
Canadians in South Park with their horizontally separated heads which bobble when talking, not to mention other ridiculously cartoonish features, even for characters in South Park.
However, the Canadian kids are actually rather cute.
Additionally, famous Canadians, such as Paul Watson and Justin Bieber, are drawn in the standard character style rather than the "Canadian-specific" character style, most likely to make them more recognizable. Céline Dion is a notable exception, as she is depicted in the "Canadian-specific" style.
Also, Sarah Jessica Parker. While every other character in the series has basically the same facial layout, she is fugly.
Not just him either; the extreme divergence of body and facial types between natives of different islands makes for some really weird-looking people.
Most of the characters from Adventure Time who don't quite fit in with the standard character design of the oUo face end up invoking this trope. Special mention goes to Xergiok, many of the monsters, the Tree Witch, and arguably, Lemongrab. In a show where most of the characters have very similar faces, the difference can be extremely jarring, and the gonks may not even appear to be from the same show.
Snips and Snails from My Little Pony: Friendship Is Magic qualify (especially Snips, who looks more like a buck-toothed piglet than anything equine). They're unicorns like some of the other mane cast but even among the colts of the series are pretty ugly, just barely bordering on Ugly Cute.
Bulk Biceps, the insanely buff pegasus (with incredibly tiny wings) from Hurricane Fluttershy easily qualifies.
Two cars in Paris in ''Cars 2'' have mismatched eyes on their windshields, have dented bodies, and crooked teeth inside their bumpers. However, a forklift artist for some reason actually decided to draw them as both being extremely attractive-looking.
Anton St. Germain and Penny from The Mighty B!. An online reviewer even stated theat Penny looks like a gorilla.
Gaia Online decided to pull a fast one on the members when asking if they wanted cute child star Timmy to remain a child or become an adult. After the votes were tallied and adult Timmy was chosen, he was aged up as promised and turned into an incredibly ugly and gangly man with an enormous honker (while everyone was expecting yet another hot anime guy). One member actually responded by posting a smiley called "gonk". The adult look was based on Nicolas Cage's character in Raising Arizona, and a surprisingly large number of users thought he was Hollywood Homely at worst. In-universe, he was able to charm a girl with a boyfriend (and got Doctor Singh into a catfight with said girl over him). Then again, there was Reapersun's Fan Disservice art of him in the man-thong from Borat...
Give the Freelance Astronauts access to a character creator and they'll make another horrifying incarnation of Dongs "REO" Speedwagon. In Oblivion she was a crone-like, green-faced, blue-haired dark elf with butterfly wings and a penchant for bludgeoning people to death with a fish. In Saints Row 2 she was an obese, slack-jawed, blue-haired woman with poor posture and a man's voice who was so disturbing that Maxwell scrapped her for Gangsta Link. And now in Mass Effect we have Dongs Shepard, with a man's head on a woman's body and something seriously wrong with her neck.