Defenceman Brad Shaw received many honors over his years in hockey, both in juniors and the NHL. After only two seasons of junior hockey, one with the Kitchener Greenshirts as a midget and the next with the OHL's Ottawa 67's, Shaw was selected 86th overall by the Detroit Red Wings in the 1982 Entry Draft, a draft that saw several future star defenceman taken, notably Scott Stevens and Phil Housley. He played for two more seasons with the 67's where he collected 160 points in 131 games over that time. He also represented Canada at the World Junior Championships, winning a bronze medal in 1983. He was named to the OHL's first All-Star team in 1984.
Before beginning the 1984-85 season, Shaw was traded to the Hartford Whalers where he began working his way up through the minors splitting time with the AHL's Binghamton Whalers and the Salt Lake Golden Eagles of the IHL. Shaw made it to the NHL with the Whalers in the 1985-86 season but spent the majority of his playing time in Binghamton. He was up and down over the next two seasons and won the Eddie Shore Award in 1987 as the AHL's outstanding defenceman. After a visit to Italy where he played for the Varese HC, scoring 40 points in 35 games, Shaw played with the Canadian National Team and played for the Whalers in the playoffs.
Finally in the 1989-90 season, Shaw started the year in the NHL with the Whalers where he was named to the all-rookie team for the year. He played two more seasons in Hartford before being traded to the New Jersey Devils where he remained for four days. The Ottawa Senators, returning to the NHL for the 1992-93 season, selected Shaw in the Expansion Draft.
Shaw played his finest season in terms of point production for the new Senators and collected 41 points in 81 games. He was named as the team's captain for the 1993-94 season. From Ottawa he moved on to the IHL where he became a player/assistant coach for the Detroit Vipers, winning the Turner Cup championship in the 1995-96 season. The next season saw Shaw named to the IHL's first all-star team.
In 1999, Shaw signed with the Washington Capitals as a free agent, where he would play only four games. He was traded to the St. Louis Blues and played eight games in the regular season and four in the playoffs. Shaw then hung up his skates and stepped behind the bench as the Detroit Vipers head coach for the 2000-01 season. The next year, he was on the move again, becoming an assistant coach with the Springfield Falcons, an affiliate to the NHL's Phoenix Coyotes and Tampa Bay Lightning.