Sanrio is mainly famous for their traditionally cute characters. But one of their most popular characters is Gudetama, who is an anthropomorphic egg that suffers from a crippling lack of motivation, rarely smiles, and has a somewhat grotesque design. He is designed for people who are tired of life to empathize with him.
The way all insects are drawn in Arrietty manages to be ridiculously cute and pretty realistic at the same time. They all have the right number of legs and beady eyes, but their portrayal is more like that of the sootspirits than something dirty or abhorrent.
Attack on Titan: A few Titans manage to fall under this, in particular the now memetic "Kawaii Titan"/Peering Titan.
Berserk: The Demon Child looks like a monstrously misshapen fetus, since he was mutated by demonic contamination while in the womb and born prematurely. You’ll probably feel sorry for the poor thing when you realize he just wants his parents to love him back. He becomes conventionally cute-looking after Griffith is reborn through him.
Bio-Meat: Nectar: Walking mouths that somehow look cute and definitely grow on you. So cute, an American couldn't shut up about it and got om-nom-nommed.
Bleach has Dondochakka and Pesche, both of whom are quite Gonk-y in terms of character design, but are nonetheless quite lovable.
Liltotto Lamperd is an inverse example. She's adorable by conventional standards, but has an ability that involves distorting her mouth into an abnormally wide maw.
L. The manga's artist, Takeshi Obata, said he was supposed to look ugly. And L has legions of fangirls (many of which compare him to a panda!). Doesn't help that the few times he smiles are genuinely endearing.
Rem is also actually quite lovely in an odd way.
Gelus looks like an abandoned rag doll. Awwww!
What's even more awesome is that in the originl designs, Gelus was supposed to be an extremely beautiful Shinigami. Ohba, however, decided that making him The Grotesque would be better because Gelus is such a pathetic figure and the audience would relate to him better. He was right!
Some fans view Hideki Ide falling under this due to his... different style of eyes.
Dai Dark: The Moja's spaceship AI, also known as Moja, is a skeletal robot dog who despite looking like a macabre doll made out a dog corpse, is very friendly and helpful toward Sanko and Avakian.
Delicious in Dungeon: The Orc Captain looks like other orcs, who are fat, muscular, and have pig-like features. She's also drawn some with cute features like round face and big eyes. Combine that with her Proud Warrior Race Guy tendency and Brutal Honesty, she won over many fans.
Several instances in Den-noh Coil. Just look at Densuke, Oyaji, or even Satchi.
Gabumon is one of the early Ugly Cute Digimon. He's a weird lizard-dog-unicorn thing, but you just want to give the guy a hug.
Guilmon would fit here too. In reality, he would look far more terrifying than cute (think Godzilla), but his childlike demeanor, antics, and voice just make him so adorable.
Renamon applies as well. The species is described in canon several times that they are tough and intimidating in appearance (especially their glaring eyes) that other Digimon become nervous or threatened by their presence despite the Renamon not intentionally trying to scare others off. This doesn't stop people, be it in the canon or in the fanbase, to still consider the race (especially female ones like Rika's Renamon) to be beautiful, elegant, cute, or (depending on who you ask) sexy.
Beerus, the main antagonist of Dragon Ball Z: Battle of Gods. His playful, cat-like nature is hard not to find endearing, and his appearance is based on a Cornish Rex◊, which would also fall into this category.
Fat Buu, post Heel–Face Turn, goes from being a vinyl toddler-minded murderer to a heroic pudgy-faced well meaning manchild. His genuine naivete helps here.
Hell, Kid Buu is kind of cute.
Krillin is short to the point of dwarfism, has no nose or chin and when he does let his hair grow out, it makes him look even goofier. Despite this, he's considered endearing enough in-universe that Android #18 gives him a playful peck on the cheek. And then they get married and have a daughter together.
Eyeshield 21loves this trope. 50% of the Devilbats are made up of Ugly-Cutes.
Fruits Basket: Kyo Sohma's true form looks like some sad mix between a bunny rabbit and a dinosaur.
Envy's true form, when stripped of all the many grotesque human souls that make up his body, is a creepy little slug-like creature with multiple legs and large eyes...and yet you just want to pick him up and snuggle him. (Note: It is highly advised that you do not snuggle him, or else he'll commandeer your body.)
Also Sloth. He's huge. He's lumpy, fanged, and freakishly dangerous. He hosts blank eyes and a vapid expression. But something about his unmotivated, drag-your-feet mannerisms and simple speech ("Mendokusai...") make him look like a perfect candidate for a plushie. His big muscles just make him look huggable. His asymmetrical design brings to mind tears like a cheetah's face. He says, "Buh?" and the readers squeal, "So cuuute!" He gets spartan-kicked off a tall building into the snow after wandering around aimlessly in a military base...the fans let out an, "Awww!"
Also, Bido. He's short, bald, and more animal-like than most of the later chimeras, with a tail and scaly skin, but he's also oddly cute. It's helped by how loyal he is to Greed and how excited he is to see Greed again after Greed has been fused with Ling.
Gundam as a whole has the Zeon-made Acguy, an aquatic mobile suit that is somewhere between "teddy bear" and "angry potato" in terms of appearances. As a result, it's not treated as much of a threat, but is widely beloved by fans precisely because it looks far too cute for a nearly 130-ton war machine. Later versions take the teddy bear motif to its logical conclusion and end up being traditionally cute.
Haré+Guu: Pokutes are kind of cute in a weird way.
Hunter × Hunter: Senritsu is nearly bald and has buck teeth, but she has a very kind heart.
Iggy from Stardust Crusaders is initially this, his appearance as that of a realistic Boston Terrier clashing heavily with the manga's art style. Subverted later on, however, as Art Evolution kicks in and he's drawn with a more human-like face, making him more traditionally cute.
Mista's Stand, Sex Pistols◊, is made up of a group of fairy like creatures that, despite not being cute in the conventional sense, end up being quite adorable.
Pesci is extremely Gonkish in appearance, but his adorable personality and relationship with Prosciutto causes many to find him endearing.
Secco mixes this and Creepy Cute, what with his exaggerated facial expression and animalistic behavior.
Aikuro's teacher disguise, with oversized sunglasses, bad posture, and scruffy hair/stubble. It's supposed to make him look like a plain middle-aged man, but some fans actually find him unbelievably sexy in it, and prefer it to his normal bishounen looks.
Senketsu manages to be one of the most adorable characters in the series despite being a sapient and rather creepy looking school uniform.
Knights of Sidonia: Tsumugi is a giant fleshy alien/human hybrid with only a vaguely humanoid body shape, lots of tentacles, and she usually interacts with others through a faceless "head-tentacle" that emerges from her abdomen and is capable of speech. Despite all this, she has the voice, personality, and mannerisms of a teenage girl. She acts innocent and friendly enough that a lot fans find her genuinely adorable.
Made in Abyss: Mitty is a small, amoeboid thing with sharp teeth, distorted features, and one large, round eye. Despite the description, she somehow manages to look huggably cute. When her backstory is revealed, she also manages to be The Woobie to an extreme extent.
A Man and His Cat: In-Universe, Kanda thinks Fukumaru, a cat everyone else passed over because he was "ugly", is cute. Naturally, he's cute to the audience too.
While most of the characters from Midori No Makibao is gonk, Makibao himself is cute- if you think of him as a hippo instead of a horse.
Tsuyu Asui is a frog girl with huge wide eyes, a wide mouth that is usually in a wide line or smile, long, semi-slimy looking black hair that sometimes blocks her eyes in a Snape-like fashion and of course, frog-like limbs and a long frog tongue. And yet she's beloved by fans because of how adorable her resultant appearance is, obviously the fact she is one of the nicest characters in the show and her Badass Adorable status helps quite a lot.
Todoroki's scarred half of his face is oftenly portrayed like that, particularly by Midoriya/Todoroki shippers.
Rock Lee and Guy-sensei (aka Thickbrows and Superbrows).
Kisame's sword Samehada, especially when it's cuddling up to Killerbee.
White Zetsu and his brother Guruguru have this going for them. Despite being villains, both are quite childlike to the point of being Affably Evil. WZ only has half a face, but likes to joke around while Guruguru is a humanoid mass of tendrils whose obsession with poo keeps him from seeming sinister even when he is being sinister.
Some of the Tailed Beasts fit this category during that brief flashback where we see them as babies.
Natsume's Book of Friends has an In-Universe example: Nyanko-sensei in his Maneki Neko form is constantly referred to ugly, "pig cat," "world's ugliest cat," etc. by nearly every character who sees him. Taki, as well as much of the fanbase, finds him absolutely adorable. The former's fangirling of him is seen as very odd by her peers and has become something of a Running Gag.
Neon Genesis Evangelion: Pen-Pen. Seriously, it's not the prettiest penguin you've ever seen (he's got clawed wings, dear God!) but what counts is how endearing he can be, especially when you know why Misato bothers to keep him despite his flaws (like being a glutton, good-for-nothing bird).
One Piece: Quite a few characters would qualify, especially Usopp, Brook, and Kumacy.
Oars Jr., despite his meteoric apparition, would qualify just in the same way as King Kong - A giant, green, gargantuan (he is at least three times bigger than your average giant!), demon-looking pirate with a soft heart (A typical run-of-the-mill Gentle Giant). He is shot, hit with a giant shockwave, had his leg severed and his heart was impaled by shadows while trying to save his friend who made him a hat that protected him from the rain.
And Marine officer T-Bone, who looks like a zombie despite being alive and well. But he's so compassionate and earnest in his desire to help people that he has the undying loyalty of his subordinates (even if they're a little creeped out by his appearance) and it's hard not to feel bad when the Straw Hats have to plow through him on their way to Enies Lobby.
For a female example, we have Kokoro's granddaughter Chimney. Some may find her more traditionally cute after the 2-year timeskip (though she's still very unique looking).
Charlotte "Marriage Proposal" Lola. To get an idea of what she looks like, let's just say there's a good reason her marriage proposals don't work out. Despite being a legitimately ugly Gonk (much uglier than the aforementioned Chimney), this is contrasted by her sweet-sounding voice and her also sweet personality. It helps that even though she's a gonk, she's drawn to be more silly and harmless looking than the creepy, evil-looking or just disturbing gonks(i.e., World Nobles, Okamas).
One-Punch Man gives us Overgrown Rover◊, a powerful, demonic, six-eyed Canis Major that has a disaster level of Dragon, second to the highest level. Originally, he isn't cute at all when he's on the hunt, being extremely feral and hostile with his targets. However, he becomes somewhat submissive after he miraculously survived being punched by Saitama. As a result, he can be commanded to sit and behaves like an actual dog, making him more approachable and downright adorable◊.
Weirdly enough, Charlotte's cake dragon from Puella Magi Madoka Magica looks cute when it's not showing off its sharp teeth.
Revolutionary Girl Utena: Chu-Chu has often been described as an ugly-cute monkey-mouse. It's a balancing act; the design itself is pretty ugly, but the way he acts can be downright adorable (or irritating; individuals' mileage may vary).
Shaman King: Chocolove is infamous for being a case of Values Dissonance, but if you look past that, he's pretty cute. In fact, his constant use of terriblepuns is borderline adorable. It kind helps that he looks a bit like the aforementioned Usopp.
Slime Life: Slime is a blob of blue goo with black dots for eyes and stubby arms and legs, yet is constantly adorable.
Space☆Dandy has the Plant Scientist's daughter, 0-33H. She is ridiculously moe-worthy despite being a sentient plant. Her reactions with Dandy are just plain adorable.
Children portrayed in Tekkonkinkreet, especially White. The art style makes it hard for anything to be stereotypically cute, but White still manages to be downright adorable at times.
Seto Kaiba's favorite card, Blue-Eyes White Dragon, isn't a "cute" monster, but in the episode where Yugi duels Johnny Stepps at Kaibaland, there's a scene (cut from the dub, sadly) with a prize machine full of plushies shaped like Duel Monsters, including an adorable BEWD plushie.
Yugi's Kuriboh plays this Trope straight, as do all of its variations. (Or maybe its simply just cute; fans are split.)
◊, which would also fall into this category.
