Babych was drafted 3rd overall by St. Louis in the 1978 NHL Amateur Draft. He played his junior career with the Edmonton Oil Kings and Portland Winter Hawks of the Western Canada Hockey League. He enjoyed some early success with the Blues but tailed off and was claimed by the Pittsburgh Penguins in 1984. He played with the Quebec Nordiques and the Hartford Whalers before retiring in 1987. He is now living in the Winnipeg, Manitoba area.