He was the second man to pole vault 15 ft (4.6 m), and is the only two-time Olympic gold medal winner in the pole vault (1952 and 1956), with a bronze medal in 1948. He also was 13th in the 1956 decathlon. While a student at the University of Illinois, Richards tied for the national collegiate pole vault title and followed that with 20 national Amateur Athletic Union (AAU) titles, including 17 in the pole vault and three in the decathlon. The first man to clear 15 feet was Dutch Warmerdam, who set the world record of 4.77 m (15 ft 73⁄4 in) in 1942, long before Richards came into his prime. While Richards was clearly the dominant vaulter of his time, he never achieved the world record.
Richards later became involved in promoting physical fitness and continued to vault in his later years. He was the first athlete to appear on the front of Wheaties cereal boxes in 1958 (though not the first depicted on all parts of the packaging), and also was the first Wheaties spokesman, setting up the Wheaties Sports Federation, which encouraged participation in Olympic sports.
Richards had four sons who also were skilled pole vaulters; Brandon, held the national high school record at 18'2" for fourteen years from 1985; Tom won the CIF California State Meet in 1988; Bob, Junior was second in the same meet in 1968 and later ranked #7 in the USA in 1973.