Just recently I was helping paint the inside of our house and of course Junior had to come by and get his ears painted when he was walking by the wall. So I decided this might be a good tip for anyone that finds themself in the same situation.
According to peteducation tar is best to leave to harden (if it is in small amounts) and then clipping it off. But when the dog gets a lot of it on his/her fur you can soak the area with vegetable oil for 24 hours so that it softens up and then washing it off with shampoo. They recommend that you bandage the area that is soaked with oil so that the dog doesn't like the oil off and thus also ingesting the tar. Never ever use gasoline, kerosene, turpentine or other organic solvents on your dog because these can have serious adverse effects on the skin.
Vegetable oil or butter is also good to remove pine pitch for those who have pine trees around their yard.
Paint is removed by letting it harden and then clipping it but Avon's product Skin So Soft can help remove oil based paints.
Summary from:
http://peteducation.com/article.cfm?c=2+2095&aid=1081