O'Bannon, a native of Corydon, Indiana, where his family owned the Corydon Democrat, attended Indiana University, with a B.A. in government, 1952, and a law degree in 1957. He also spent two years in the United States Air Force. He was chairman of the board of the family newspaper publishing firm until the time of his death.
First elected to his father's seat in the Indiana state senate in 1970, where he was the primary sponsor of legislation reintroducing the death penalty , he became lieutenant governor in 1989 when Evan Bayh was elected governor. In 1996, when Bayh had a successful campaign for the U.S. Senate, O'Bannon ran for governor. He overcame an early deficit against his Republican opponent, Indianapolis mayor Stephen Goldsmith and won in a close race. He was re-elected in 2000.
During the boom years of the 1990s, when Indiana amassed a record $2 billion surplus, O'Bannon was able to cut taxes by $1.5 billion, hire 500 more police officers in the state and win increased funding for schools and extended health insurance for poor families. In 2000 he won an easy re-election bid.
After the market downturn, however, Indiana lost 120,000 jobs, tax revenues dropped, and O'Bannon had to cut social services in order to spare education. In 2001 he worked with the state legislature to formulate a major restructuring of the state tax system. His opponents blamed him for botching the state's finances. They pointed to an embezzlement from a public retirement fund, a slow response by his environmental agency to a big fish kill, and problems at two state centers for the developmentally disabled. But no one ever doubted his probity and folksy charm.
On September 8, 2003, O'Bannon was in Chicago, Illinois attending the U.S. Midwest-Japan trade conference when he suffered a massive stroke. He was taken to Northwestern Memorial Hospital. His condition worsened and based on his living will, his family decided to use no further means of support and care. He died on September 13, 2003, leaving behind his wife Judy (Asmus), three children (Polly, Jennifer and Jonathan) and five grandchildren.
He was succeeded by Lieutenant Governor Joe Kernan.