Any increase in physical activity can create stresses on canine bodies, as well as human bodies. Before you start a new physical exercise routine, including running, get a checkup with your doctor and take your dog to the vet for a once over. Some dogs, like pugs, may have respiratory, overheating or joint-related issues that should be understood before you attempt to run with them.
You should also get legal. That means making sure your dog is current on his inoculations and is licensed in accordance with the laws in your state.