One of my parents' dogs has a big smile. She'll be panting with her mouth wide open, but when she sees me, she draws the corners back even further and comes running up with her tail wagging. She has a very long nose and wide mouth, so seeing her pull her lips back and her cheeks wrinkle with dimples (as intothebleach's Carling) is very funny.
My chihuahua also does an "Elvis lip curl" occasionally. He does it mostly when he's feeling playful. He'll toss a ball at me or bark to get my attention and then keep one of his chops up, showing a few of his teeth on one side. He also seems to smile with his mouth closed, simply pulling his mouth back and putting his ears up, as though he's quietly laughing at me!
There's also something called the submissive grin, in which dogs will expose their teeth or "smile."
Quote:Some dogs show a “submissive grin” when they’re feeling extremely submissive. They pull their lips up vertically and display their front teeth (canines and incisors). This signal is almost always accompanied by an overall submissive body posture, such as a lowered head, yelping or whining, and squinty eyes. Only some dogs “grin” this way. People sometimes mistakenly think a dog is being aggressive when, in fact, he’s grinning submissively and trying to communicate the exact opposite of aggression.