Tick Tock the Crocodile from Disney's adaptation of Peter Pan. On the one hand, he's a crocodile with a taste for human (in this case Captain Hook's) flesh with razor sharp teeth. On the other hand, he's so goofy-looking and his antics with Hook are so funny that you can't help but find him endearing.
The penguins, after they've been mutated, are supposed to be hideous monsters, and although they possess a Sickly Green Glow and mismatched body parts, but are still, well, penguins. Especially Private, whose only monstrous traits are a purple tint and a pair of antlers.
Dave could also be considered as this, especially after he is hit by the reversed ray, turns into a cuter version of himself. His octopus assistants are also somewhat cute with the bubbly sounds they make.
Scrat from Ice Age probably qualifies with that long snout, big eyes and pointed fangs of his. The fact that he's essentially the film's equivalent of Wile E. Coyote probably helps.
Sid is also very weird looking with his wide-set eyes, big nose, and crooked teeth all the way down to his slothy hips. He's clumsy, awkward, and is voiced by John Leguizamo in a tone that goes from normal with a lisp to shrill and girly. Everything about him is absolutely huggable.
The eponymous Boxtrolls from The Boxtrolls, are little, dirty, gray creatures who wear boxes and only come out at night. They have grubby fingers, large teeth, and eyes that glow in the dark. They are also terribly timid, have very innocent motivations, and have the cutest little voices.
The various goblins from Strange Magic, especially after their king falls in love once you get used to their appearance.
Some fans of Corpse Bride consider the title character, Emily, to be rather cute for a rotting corpse in a tattered wedding dress whose eye occasionally falls out.