Considered a franchise talent after a standout junior career in the Western Hockey League (WHL) with the Portland Winter Hawks, Babych was selected second overall in the 1980 NHL Entry Draft by the Winnipeg Jets.

Babych stepped into the Jets lineup immediately as a teenager during the 1980–81 season, turning in a stellar rookie campaign in which he finished second on the club with 38 assists and led all Winnipeg blueliners with 44 points.

Unpopular with Winnipeg fans at the time, the move would be a terrible one for the Jets as Neufeld was never more than a depth player for them and was out of the NHL by 1989, while Babych continued to excel for nearly another 15 years.

In Hartford, Babych continued his stellar play, finishing the season with 69 points - the second-highest total of his career - and was named the team's top defender.

After missing almost all of the previous season to injury, Hartford exposed Babych in the 1991 NHL Expansion Draft, where he was selected by the Minnesota North Stars.

While Babych was no longer the front-line defender he was earlier in his career, he continued to be a steady and valued contributor during his seven years in Vancouver, capable of showing flashes of his former offensive ability.

He finished the 1991–92 season with five goals and 29 points (second amongst Vancouver defenders, behind Jyrki Lumme), and was a key factor on a vastly improved Canuck team which won their division for the first time in 17 years.

After the Rangers came back from a 3–0 deficit to tie the game, Babych jumped into the rush and buried a pass from Pavel Bure to score the game-winning goal.

However, Babych missed a substantial amount of time after breaking his foot blocking a slap shot soon after his arrival in Philadelphia, and the Flyers were knocked out of the playoffs in the first round.

[1] In December 2009, he was hired to work in a part-time capacity with the Vancouver Canucks as an assistant specializing in defencemen to director of player personnel Dave Gagner.

[1] Babych sued the Flyers and the team's orthopedic surgeon, Dr. Arthur Bartolozzi, in 2002, claiming that improper medical care for his 1998 foot injury shortened his career.