Davis singlehandedly led his team to the 1954 Class A Ohio high school track and field championship, scoring all 20 of Barberton's points. Davis won the 220-yard dash, the broad jump and the 180-yard low hurdles – setting a then-state record in that event – while also placing fourth in the 100-yard dash. His point total placed him ahead of Mansfield, which scored 14 points in the meet and took second. He was offered more than 200 athletic scholarships for college, and chose to attend Ohio State University.
Davis was either at or close to world records in many events including: 100 yards/meters (9.6/10.3), 200 meters (21.0), the half mile (1:52), 120 yard high hurdles (14.0), 200 meter low hurdles on curve (22.5 WR), 400 meter intermediate hurdles (49.2 WR), high jump (6-8), and long jump (24'8"). He, Felix Sanchez, Angelo Taylor and Edwin Moses are the only four hurdlers to have won the Olympic 400 meter hurdles twice. However Davis is the only man to have set world records in the quarter mile with hurdles and without. His coach Larry Snyder, who also had coached Jesse Owens, said that Davis was possibly a greater talent than Jesse Owens.
Davis won a third gold medal as a member of the United States 4 x 400 meter relay team in 1960. He set world records in both flat and hurdle races. He is a member of the United States Olympic Hall of Fame.
Davis was a longtime resident of Barberton, Ohio, teaching and coaching there for 33 years, and was the owner of Jeep's Olympic Driving School. Prior to this, Davis was a popular teacher at Barberton High School and part owner of one of the students' favorite gathering spots, Jeep and Joe's Pizza. He also loved to play the harmonica.
He was sometimes confused with Heisman Trophy-winning football player Glenn Woodward Davis (1924–2005). The two sportsmen occasionally received each other's mail, but they never met.