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, with the popular fan chant of "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, Smith stated that he would never wear 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.
