Young was a two-time Stanley Cup winner and helped the United States to a silver medal at the 2002 Salt Lake City Olympics and a first-place finish at the World Cup of Hockey in 1996.

The Hartford Whalers selected Young, a forward from Clinton, Massachusetts, with the No. 11 pick of the 1986 NHL Draft after he scored 16 goals in his freshman season at Boston University to earn Hockey East Rookie of the Year honors. He scored 15 goals as a sophomore, then joined the U.S. National Team and played in the 1988 Calgary Olympics before joining the Whalers and playing his first NHL game March 2, 1988, against the Chicago Blackhawks.

Young scored 19 goals as a rookie in 1988-89 and 24 the following season. But he struggled during the first half of 1990-91 and was traded to the Pittsburgh Penguins on Dec. 21, 1990. He scored 11 goals in 43 regular-season games after the trade and contributed seven points (one goal, six assists) in 17 Stanley Cup Playoff games during Pittsburgh's run to its first Stanley Cup championship since entering the NHL in 1967.

However, Young wasn't around for the repeat in 1992. Instead of returning to Pittsburgh, he played in Italy, then rejoined the U.S. National Team and played at the 1992 Albertville Olympics. The Penguins traded him to the Quebec Nordiques on March 10, 1992, and he scored 30 goals in 1992-93. He played two more seasons with Quebec, accompanied the Nordiques when they relocated to become the Colorado Avalanche in the summer of 1995. He scored 21 goals in 1995-96, then contributed 15 points (three goals, 12 assists) to help the Avalanche win the Stanley Cup. That summer, he scored two goals in seven games to help the United States win the World Cup of Hockey

The Avalanche traded Young to the Mighty Ducks of Anaheim on Sept. 17, 1997, and after one season he signed with the St. Louis Blues as a free agent July 16, 1998.

Young scored 24 goals in each of his first two seasons with the Blues, then scored an NHL career-high 40 in 2000-01. His 73 points were also an NHL single-season high. He played one more season with the Blues and helped the United States win silver at the 2002 Salt Lake City Olympics before signing with the Dallas Stars as a free agent July 5, 2002. Young returned to the Blues as a free agent Sept. 13, 2005, and led St. Louis with 49 points (18 goals, 31 assists) in 2005-06, but they finished last in NHL and he retired with 757 points (342 goals, 415 assists) in 1,181 NHL games and 87 points (44 goals, 43 assists) in 141 Stanley Cup Playoff games. He was inducted into the U.S. Hockey Hall of Fame in 2017.