A hangdog look is one that betrays a feeling of shame, embarrassment, or fear. Your hangdog expression after sneaking a whoopee cushion onto your teacher's chair is a dead giveaway that you're guilty.
Use the adjective hangdog to describe someone's cowering appearance or the sheepish look on her face. You might have a hangdog look if you're afraid of getting in trouble, or if you regret your actions. The now-obsolete root noun hang-dog was used in the 17th century to mean "a despicable, low person," or someone who's "only fit to hang a dog," or sometimes "only fit to be hung (like a dog)."