Spaziani is a native of Clark, New Jersey, and a graduate of Arthur L. Johnson High School. Spaziani played quarterback and linebacker for the Penn State Nittany Lions from 1965 to 1968. He was a member of the team that went to the 1967 Gator Bowl and also played in the team that went to the 1969 Orange Bowl. He was the subject of one of Joe Paterno's notable early quotes: the Nittany Lions' coach said of Spaziani, "Don't get the idea that I like him because he's Italian. I like him because I'm Italian." Spaziani was also a starting pitcher for the Penn State baseball team.