Cassady played football for the Ohio State Buckeyes from 1952 to 1955. During his college career, he scored 37 touchdowns in 36 games. He also played defensive back; a pass was never completed on him in his four years at the university. He was twice selected as a unanimous All-American, in 1954 and 1955. The 1954 Buckeyes finished the season 10–0 and won a consensus national championship. That year Cassady finished third in the vote for the Heisman Trophy, behind Alan Ameche of Wisconsin. In 1955, he won the Heisman Trophy (by the largest margin at the time) and the Maxwell Award, and was named the Associated Press Athlete of the Year. During his playing days, he was 5'10" and 170 pounds.
Cassady earned the nickname "Hopalong" during his first game as a freshman for Ohio State. Columbus sportswriters who saw him play said he "hopped all over the field like the performing cowboy", a reference to the fictional character Hopalong Cassidy. In that game, Cassady came off the bench to score three touchdowns in a win over Indiana University.
During an Ohio State practice in 1953, Cassady was having trouble executing an off-tackle run. At this point Coach Woody Hayes told Cassady to take a seat and brought in backup running back Robert Croce, who executed the play flawlessly and carried the ball for 20+ yards. Hayes then told Cassady, "Cassady, did you see that Croce was just slow enough to hit the hole. You're hitting the line too fast!"
Cassady held some Ohio State career records for many years following his graduation. He held the career rushing record (2,466 yards) until it was surpassed by Jim Otis in 1969, the career all-purpose yards record (4,403 yards) until surpassed by Archie Griffin in 1974, and the scoring record (222 points) until surpassed by Pete Johnson in 1975.
Cassady also played baseball for Ohio State. He led the team in home runs in 1955, and stolen bases in 1956. He also became a member of the Sigma Chi fraternity there.
Cassady played eight seasons in the National Football League: seven (1956–1961, and 1963) for the Detroit Lions, and one season (1962) split between the Cleveland Browns and the Philadelphia Eagles. In the NFL he was an all-purpose back, playing both receiver and running back and scoring 27 career touchdowns.
After football
After retiring from football, Cassady became an entrepreneur forming a company manufacturing concrete pipe. He then served as a scout for the New York Yankeesbaseball team, and as the first base coach for their former AAA affiliate, the Columbus Clippers.