Babych became the first NHL player to wear No. 44 regularly; in fact, the Edmonton-born defenseman wore it for every one of his 1,195 NHL games with five teams during a career that lasted 19 seasons.

The Winnipeg Jets, a former World Hockey Association team coming off their first season in the League, selected Babych with the No. 2 pick of the 1980 NHL Draft after a 22-goal, 82-point season with Portland of the Western Hockey League. It came two years after his older brother, forward Wayne Babych, was taken by the St. Louis Blues with the No. 3 pick of the 1978 NHL Draft.

Though the Jets finished last in the NHL (9-57 with 14 ties) in 1980-81, Babych was one of their few bright spots, with 44 points (six goals, 38 assists) in 69 games.

The addition of two future Hockey Hall of Famers, rookie center Dale Hawerchuk and veteran defenseman Serge Savard, for the 1981-82 season led to major improvement by the Jets and Babych. Winnipeg qualified for the Stanley Cup Playoffs for the first time, and Babych scored an NHL career-high 19 goals. In 1982-83, he had NHL career highs in assists (61) and points (74) and was selected to play for the Campbell Conference at the 1983 NHL All-Star Game.

Babych led the Jets in scoring with nine points (two goals, seven assists) during the 1985 playoffs, when they advanced to the Smythe Division Final, and he had 16 points in their first 19 games in 1985-86. However, the Jets traded him to the Hartford Whalers on Nov. 21, 1985. Babych continued to be among the most productive defensemen in the NHL for the next five seasons, leading Hartford's defensemen in points each time.

That streak came to an end in 1990-91, when Babych missed all but eight games because of a wrist injury that required surgery. The Whalers exposed him in the 1991 NHL Expansion Draft; he was claimed by the Minnesota North Stars but traded to the Vancouver Canucks on June 22, 1991.

Babych was no longer a big producer offensively, but he remained a steady contributor and played a valuable role in Vancouver's run to the 1994 Stanley Cup Final, contributing eight points (three goals, five assists) in 24 games before the Canucks lost to the New York Rangers in seven games. He remained with Vancouver until being traded to the Philadelphia Flyers on March 24, 1998. The Flyers traded him to the Los Angeles Kings on March 23, 1999, and he played eight games for the Kings before retiring from the NHL with 723 points (142 goals, 581 assists) in 1,195 games and 62 points (21 goals, 41 assists) in 114 playoff games.

After retiring, Babych returned to the Canucks in a variety of roles, including assistant player personnel director.