Breckenridge is a city in Stephens County, Texas, United States. The population was 5,780 at the 2010 census. It is the county seat of Stephens County. The mayor is Jim McKay.Breckenridge was a stop on the since defunct Wichita Falls and Southern Railroad, one of the properties of Frank Kell and Joseph A. Kemp of Wichita Falls, Texas. The line was thereafter operated until 1969 by the Chicago, Rock Island and Pacific Railroad.Former Texas State Representative Carl Isett of Lubbock was born in Breckenridge in 1957.Dallas Cowboys legend and Texas High School Football Hall of Fame member Gerald M. "Jerry" Tubbs was an honor graduate student and played center at Breckenridge High School. He was part of two Texas state championship football teams in 1951 and 1952. He played in three high school All-Star games and was a unanimous Texas All-State selection in 1952. In 1971, Tubbs was inducted into the Texas High School Football Hall of Fame.