Soon after graduation, Goddard enlisted in the United States Army Air Corps as a private for World War II service. He was commissioned by the Air Corps in 1942 and served as an operations and communications officer in England, India, North Africa, and the South Pacific. He was discharged from the Air Corps in 1946 as a major, remained active in the Air Force Reserve, and rose to a final rank of colonel.
Goddard married Julia "Judy" Hatch of Springfield, Illinois in 1944. The couple choose to settle in Arizona upon a doctor's recommendation that the dry climate would help relieve Judy's rheumatoid arthritis. The marriage resulted in three sons, Terry (the current Attorney General of Arizona), Tim and Bill. Goddard earned his law degree at the University of Arizona in 1949 and began practicing in Tucson.
Goddard became a widower in 1999 and was survived by all three sons and his second wife, Myra Ann.
He first was elected chairman of the Arizona Democratic State Committee in 1960. In 1961-1962 he served as president of the 11 state Western Conference of United Funds. He became recognized as a rising power in Democratic politics in the state and in 1962 made an unsuccessful bid for the governorship. He ran for governor again in 1964, and this time won, beating future U.S. Attorney General Richard Kleindienst by 53%-47%. Goddard's campaign symbol, the Arizona roadrunner, became familiar throughout the state, and it helped bolster his reputation as a man of energy who got things done.
As Governor, Goddard helped to organise a compromise amongst regional governors supporting the Colorado River Basin Project including the Central Arizona Project. This secured a reliable water source for the state, providing a foundation for the subsequent rapid economic population and economic growth that has occurred.
Governor Goddard signed a bill banning discrimination on grounds of race, gender, religion and ethnicity. He also established the state's first budget office and worked to improve relations with the Mexican state of Sonora.
He stood for re-election in 1966 but was defeated by Jack Williams, and lost to Williams again in 1968. Goddard also served as chair of the Arizona Democratic Party for 10 years and on the Democratic National Committee for 20 years.