A forward, Thompson had a long playing career and club level, making 487 appearances and scoring 124 goals in the Premier League and throughout the Football League. His peak years were earlier in his career with Coventry City, for whom he scored 49 goals in 158 appearances and West Bromwich Albion, for whom he was voted the club's 1984–85 Player of the Year. Late in the 1989–90 season Thompson joined Crystal Palace to provide cover for the injured Ian Wright, but was cup-tied for the 1990 FA Cup Final. He briefly played in the Premier League for Queens Park Rangers during the 1992–93 season and made one European appearance for Cardiff City in September 1993. Thompson retired at the end of the 1996–97 season and finished his career with 584 appearances and 153 goals.