Galley played at Bowling Green (CCHA) from 81–82 to 83–84 and was named to the CCHA first all-star team and NCAA All-American in 1984. Galley was drafted 100th overall (5th round) by the Los Angeles Kings in the 1983 NHL Entry Draft. He played in 1,149 career NHL games, scoring 125 goals and 474 assists for 599 points. He also registered 1,218 career penalty minutes. His best offensive season was the 1993–94 season, when he registered 60 assists and 70 points, both career highs.