Smith played college football at Michigan State University. He was awarded with All-America honors in 1965 and 1966. In his senior season, he played in the "Game of the Century" (a 10–10 tie at home against the University of Notre Dame). Michigan State finished 2nd in the voting for the National Championship, behind Notre Dame. In 1988, Smith was enshrined in the College Football Hall of Fame. Smith was a popular athlete at Michigan State, earning the slogan "Kill Bubba Kill."

Michigan State retired his number 95 jersey on September 23, 2006, prior to the Spartans' home game against Notre Dame, amid repeated cheers of his old slogan from the student section. This game also celebrated the 40th anniversary of the "Game of the Century".

Smith spent nine seasons in the NFL as a defensive end. He was the first overall selection in the 1967 NFL draft, chosen by the Baltimore Colts. The Colts won Super Bowl V at the end of the 1970 season, earning Smith his only Super Bowl ring. However, in interviews, he has stated that he never wears the ring, as it was seen as a "sloppy" game by many. He was traded to the Oakland Raiders before the 1972 season, and finished his career with the Houston Oilers. He was selected All-Pro one year, All-Conference two years, and went to two Pro Bowls.

After leaving professional football, Smith began his acting career in small movie and television roles in the late 1970s and early 1980s. He is perhaps best known for his role as Moses Hightower in the Police Academy movie series, a role he has reprised in all but one of the Police Academy sequels. He is the long time spokesman of Baltimore area law firm Cohen, Snyder, Eisenberg & Katzenberg. Smith starred in the short-lived television series Blue Thunder, partnering with fellow Pro Football Hall of Fame defensive star Dick Butkus.

His late brother Tody Smith played for the University of Southern California and for the Dallas Cowboys, Houston Oilers and Buffalo Bills.

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