Can you get rabies from a dog if he got very close to you but didn't bite you?

No, very unlikely: A dog would not transmit rabies to a human without biting the human, unless the dog coughed or sneezed, and it's saliva flew through the air and landed on the human's eyes, nose, mouth, or skin wounds. The virus is in the dog's saliva.

No: Rabies enters the body by a puncture wound from an infected animal. It is not passed by contact of any sort if the surface of your skin is intact. The dog you were close to probably did not have rabies anyway. The most common source of rabies in the USA is bat bites.

No dog rabies in U.S: The CDC declared the U.S. free of rabies in dogs. That's because most dogs are vaccinated, & the virus has 'no where else' to live in the dog population. There are other risks though -particularly bites of wild animals, incl. 'wild dogs'. If this dog was owned by someone- call the owner. For rabies to be transmitted, a bite or scratch is needed. Saliva in the eyes/mouth would be extremely rare.

NONBITE: There is what's called "non-bite exposure", but this is not one of them. You cannot get rabies petting a rabid dog.

Nope: Rabies is a preventable viral disease of mammals most often transmitted through the bite of a rabid animal. The vast majority of rabies cases reported to the Centers for Disease Control and Prevention (CDC) each year occur in wild animals like raccoons, skunks, bats, and foxes. http://www.cdc.gov/rabies/index.html