Run, Joe, Run (TV series)

Joe, a trained member of the military's K-9 corps, was falsely accused of attacking his master, Sergeant Corey. Joe managed to escape before being killed and a bounty was put on his head. While Sergeant Corey tried to find him before the authorities did, Joe managed to help the people he encountered on his travels. Although Corey always came close, he never managed to find Joe. During the second season, Corey was called back to duty and Joe teamed up with Josh McCoy, a hiker, and continued on his trek while helping others. - IMDb