One of my dog enjoys physical contact of any kind - petting, scratching, patting and especially hugging. I have never met a dog that likes hugs as much as Dakota does.
On the flip side, I have a dog who doesn't enjoy petting very much. He accepts it, but he isn't happy about it until he gets a butt scratch.
Both of my dogs completely melt if I do what Smkie mentioned and rub right behind their ears, and both of them looove getting their butt (not literally their butt, but that's what we call the area around their hips) scratched. We recently introduced Ripley to the bamboo back scratcher and if we hold it over him, he'll start doing this weird little writhing movement to self-scratch. It's hilarious.