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.
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.
He 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.
Richards is referenced in the ESPN 30 for 30 documentary Survive and Advance, for the impact he had on former N.C. State coach Jim Valvano. Valvano cites hearing Richards speak when he was a teen and the motivational messages he implored. The coach, who died in 1993, led the Wolfpack to one of the biggest upsets in tournament history, beating top-ranked Houston in the 1983 NCAA title game at the Pit in Albuquerque.