Godfrey learned to fly in 1929 while working in broadcast radio in the Washington, D.C., area, starting with gliders, then learning to fly airplanes. He was badly injured on his way to a flying lesson one afternoon in 1931 when an oncoming truck lost its left front wheel and hit him head on. Godfrey spent months recuperating, and the injury kept him from flying on active duty during World War II. He served as a reserve officer in the United States Navy in a public affairs role during the war.