Along that vein (and created in the same town as the Sock Monkey was—seriously, we have giant plexiglass sock monkeys and a sock monkey wing in the museum): The adorable creepy/ugly-cute of the Socks That Rock line.
Mutant Dolls. Basically ragdolls with huge eyes, horns, fangs, floppy, lopsided bodies, and and odd, vacant stares - and you just wanna hug 'em?
The legendary "Robert The Doll" would fit in this trope. Sure, he's a haunted doll rumored to curse you if you don't ask him permission before taking his picture, but he is kinda cute http://www.robertthedoll.org/
The Worrible. Weird, bulgy-eyed, drooling, round, yet somehow adorable little...thing.
Squishables has made plush versions of all sorts of oddly adorable creatures from octopi to jellyfish to axolotl to even Cthulhu. Yes, there's a squishy Cthulhu.
This is pretty much the explanation for the success of Troll dolls.
The My Pet Monster toy line (and associated media) from the 1980s was a deliberate attempt to invoke this trope, especially with the "My Monster Pet" toys, which were more dog-like. The 2001 Toymax version retooled the Monster making him more conventionally cute, but still falling into this trope.