You don't know what types of hazards you'll encounter on a run, so be prepared. Run with your dog in familiar areas, and know where you are and how to find help at all times. Carry a cell phone for emergencies.
Feral animals or pets that are roaming unattended can be dangerous, so recognize the potential problems and act swiftly to get your dog and yourself out of harm's way. You can provide added protection by carrying a large stick with you, and even keeping a few dog treats on hand to direct a threatening dog in the opposite direction and buy time to make a quick getaway. It also pays to carry gear like pepper spray, a loud whistle or other handheld devices that may be legal in your area.