Williams was born on September 26, 1932 in Mobile, Alabama, to parents Clifton Curtis Williams and Gertrude (née Medicus) Williams. He was active in the Boy Scouts of America where he achieved its second highest rank, Life Scout. Williams attended Murphy High School in Mobile, from which he graduated in 1949. He received a Bachelor of Science degree in Mechanical Engineering from Auburn University (AU), Auburn, Alabama in 1954. Having joined the Navy ROTC while at AU, he was commissioned a Second Lieutenant in the Marine Corps on August 9, 1954.  His hobbies included hunting, golf, and water sports.

Following flight training, he served with operational tactical jet squadrons of the Fleet Marine Force. He then attended the U.S. Naval Test Pilot School at NAS Patuxent River, Maryland. Following graduation from USNTPS, he was test pilot for three years in the Carrier Suitability Branch of the Flight Test Division at NAS Patuxent River. His work there included both land-based and shipboard tests of the F-8E, TF-8A, F-8E (attack), and A-4E aircraft and the automatic carrier landing system (ACLS). While at NAS Patuxent River, he was selected for the NASA astronaut program in the third group of prospective Gemini and Apollo astronauts in late 1963.  Of the 2,500 hours flying time accumulated, he has more than 2,100 hours in jet aircraft.

On October 18, 1963, Major Williams was named by NASA as one of their third group of astronauts, along with thirteen others. This group included Buzz Aldrin, who took part in the first lunar landing in 1969, as well as Roger B. Chaffee, who died in the Apollo 1 fire in 1967.  Williams served as the backup pilot for Gemini 10, which took place in July 1966. Later that year Pete Conrad chose Williams to be the Lunar Module Pilot on the mission for which Conrad was Commander, which would serve as the back-up Apollo 9 crew, and later become Apollo 12. After his death, his position on Conrad’s crew was filled by Alan Bean, who had been his Commander on the Gemini 10 backup crew.

When Williams was named an astronaut, he held the distinction of being the only bachelor in the group. This changed when he married Jane Elizabeth Lansche (known as “Beth”), who was a former waterskiing performer at the Cypress Gardens theme park in Florida. Upon the announcement of their engagement, the press feigned disappointment over the loss of the nation’s only bachelor astronaut. The couple met in June 1957. They were married on July 1, 1964, in St. Paul’s Catholic Church in New Bern, North Carolina, which was Lansche’s hometown. The couple had two children. Their first daughter, Catherine Ann, was born on January 6, 1967. Their second daughter, Jane Dee Williams, was born on May 31, 1968, nearly eight months after Williams had died.

Williams died after a mechanical failure caused the aileron controls to jam on his T-38 jet trainer near Tallahassee, Florida on October 5, 1967. His plane went into an uncontrollable aileron roll while he was flying from Cape Canaveral to Mobile, Alabama, en route to see his father who was dying of cancer. The aircraft dived straight down, between pine trees 30 metres (98 ft) apart, and crashed without touching them, although it did singe them from a fire caused by the crash. According to an Air Force spokesman, Clifton’s plane disintegrated. The jet was flying at 6,800 metres (22,300 ft) when it performed a sudden roll to the left and dived into the ground, almost straight down, at 1,125 kilometres per hour (699 mph). Williams ejected at 450 metres (1,480 ft) altitude, but the plane was traveling too fast at too low an altitude for the seat to land safely.