After graduating from Lash High School in Zanesville in 1943, Taylor entered the United States Army Air Forces where he served from 1943 to 1946. Despite never having played high school basketball, he became an outstanding player at Ohio State and was the starting forward on the 1950 Big Ten Conference championship basketball team. In addition he was Ohio State University's first All-American baseball player. His number 27 is now retired at Ohio State.
Taylor returned to Chattanooga in 1951, this time batting .291 in 152 games. He again earned a brief trial with the Senators, appearing in six more games. In 1952, he managed to play in ten games while again spending most of the season in the minors. After playing one more season with the independent Beaumont Explorers of the Texas League in 1953, he left baseball for good.
After the end of his baseball career, Taylor returned to Ohio State as assistant basketball coach in 1958, becoming head coach the following year.
During his 18 years at Ohio State, the Buckeyes won the 1960 NCAA championship, were finalists in 1961 and 1962 and claimed a third place finish in 1968. The last time he coached the Buckeyes to an NCAA tournament appearance was in 1971, where OSU upset previously unbeaten Marquette in the Mideast regional semifinal round. However, Western Kentucky beat OSU in the Mideast regional round to advance to the Final Four. In his five NCAA tournament appearances, Taylor's teams went 14–4 and also won or shared seven Big Ten titles.
Taylor finished his career with an overall record of 297–158 and was named Coach of the Year by the USBWA and UPI in 1961 and 1962. A talented recruiter, Taylor coached six All-Americans as well as Hall of Famers Jerry Lucas, John Havlicek and Bobby Knight.
After retiring from coaching in 1976, Taylor managed the U.S. National Team in the 1978 FIBA World Championships and the 1979 Pan American Games. In addition, Taylor managed The Golf Club, a private golf course in New Albany, Ohio for 18 years.