He played in 1,149 career NHL games, scoring 125 goals and 474 assists for 599 points.

Galley played two and a half seasons (84–85 to 86–87) with the Los Angeles Kings before being traded to the Washington Capitals in February 1987.

In Game Two of the 1990 playoff series against Montreal, Galley scored the game-winner in overtime.

Galley played for Canada at the 1993 World Championship in Munich, where the Canadian squad placed fourth (8-1-2-3-0) under head coach Mike Keenan.

He won silver (losing to the Czech Republic 4–2) in the World Men's Championship (IIHF) in 1996 under head coach Tom Renney.