Cloudscratcher has Toosus, which have the body structure of a spider, and the texture of a puppy.
Several examples in The Inexplicable Adventures of Bob!. Molly's pet Snookums is a space monster Bob calls a "tentacle bunny". Molly herself is a pretty weird-looking creature. Roofus the Robot would not be especially cute if not for his innocent personality; well, okay, the construction-worker cap built into his head is kind of cute. And Voluptua, even in her alien butterfly form, still manages to be very attractive.
This is a common theme in Digger, as well as Ursula Vernon's other work. Currently she's on a kick of making adorable phalloi — which are Greek fertility symbols that are basically penises with wings and feet.
Plus, her relationship with Gamma is very, very sweet. I couldn't help but go "awww" when Zimmy and Annie arrived where Gamma was in Zimmy's dark, terrifying hallucination (which seems to come right off a Silent Hill game), and Gamma was sleeping peacefully on top of a giant pile of cute, brightly colored stuffed toys, representing just how much she means to Zimmy.
Tchick the Beholder in Planescape Survival Guide. He's a giant floating eyeball who has extra eyes on stalks around his bulbous body. And all the other beholders won't even let him play their beholder games!
Squidge the bogeyman in Tales of the Questor is somewhat reminiscent of Gollum and Stitch, both mentioned elsewhere on this page.
Some of the lusii may count too. Tinkerbull is under this category, though he's more just plain adorable. Aurthour, the weird-looking centaur-cow-man lusus of Equius, fits better. He's definitely not cute by normal standards, but his mannerisms help him to achieve a similar effect.
Kanaya's lusus definitely falls under this. It's basically a truly gigantic winged bug with a skull for a face. But she's such a caring guardian to Kanaya! Look at her as a spritecomforting Kanaya◊. And Kanaya mentions reading stories to her on 12th Perigee's Eve. Aww.
This is the only way to describe how Calliope looks. One is led to believe that she is a different and more attractive-looking species right up to her reveal, making your first reaction be "What the hell is that thing!?", but then you realize that she's adorable.
About half the fanbase thinks her brother Caliborn, the juvenile form of LordEnglish, is almost as adorable. How can you honestly take this face◊ seriously as that of the angel of double-death?
And the imps. Easy to kill, but how can you hate them?
Some of the members of the Midnight Crew and the Felt are rather endearing-looking in a cartoony sort of way, despite being alien gangsters. Clubs Deuce especially so.
Lovely Lovecraft: Phil in his Earthly form is almost cute, and presumably the other Night Gaunts are too.
Bort from Dominic Deegan, who seems to be one of the few characters that the Hatedom itself accepts.
Choo Choo Bear from Something*Positive has to fall under this trope. A hairless cat, over thirty years old, whose cancer treatments in his younger days reduced his bones to a gelatinous substance that let him contort into various shapes and travel through sewage pipes. He's a bit of a freak, but he's so %*!& cute that he gets forgiven for just about anything he does, up to and including suspected murder.
It's yet another horrible death trap of fun in the Axe-Crazy building Castle Heterodyne, but the Nyar spider is just so cute (it even eats its victim with a little knife and fork.)
Due to the art style, many normally horrific monsters can turn out this way in The Order of the Stick. For example, Tsukiko apparently sleeps with a plushie version of Xykon, and the instant that comic appeared all the fans wanted one. For context, Xykon is an undead Magnificent Bastard. He's also an adorably drawn stick figure skeleton with expressive glowing eye-sockets, a cheerful-looking skeletal grin, and a little golden crown floating just above his head. In plushie form, too cute for words.
Chelsea Grinn of Chimneyspeak is a ravishing young woman... who's covered with scars and is utterly psychotic... and still is adorable in her own way.
Pretty much all of the hellhounds in Wurr. Underfed, deformed doggies never looked so cute.
The title character of Selkie is an orthodontic nightmare with Hellish Pupils and a bluish skin tone more commonly associated with walking corpses. She describes herself as "a pretty one", and the fans are inclined to agree. (The tipping points seem to be that a): she has normal human hair, and b): apart from the fangs, her smile is the same as that of any other Heartwarming Orphan.)
The characters in Catana Comics are all drawn in a very simplistic design that features round heads, bulging round eyes, and tiny mouths almost between their eyes. However, it somehow works quite well and gels with the incredible wholesomeness of the comic's content.