When watching a creature feature, I usually root for the monster.
I get excited about a fierce character design, and the characteristics it possess for potential mayhem. Sure, no one would want Godzilla to destroy THEIR house, but it's pretty satisfying to see him topple rows of buildings with a mere tail swipe.
I love the idea of creating things that amuse and revolt all at once (Garbage Pail Kids, anyone?). The creature from The Thing was all sorts of terrible, but I watched every moment with rapt attention. What new, repulsive shape would it manifest? When I want to appreciate the melding of cute and bizarre, I look no further than the work of Brian Froud. His Fireys in Labyrinth were fodder for nightmares. They still make my skin crawl a little, even as an adult.
I'm pretty new to sculpting, and equally novice at creature design. It's exciting to plumb the depths of my childhood imagination, and refine ideas with adult eyes. When sculpting a new piece, my aim is typically to trigger delight and disgust. Does it make you uncomfortable? Something is working. Does it make you laugh at the same time? Even better!