Kolzig was born in Johannesburg, South Africa to German parents (he played internationally for Germany), but grew up in Canada, including in Union Bay, British Columbia when he was a teenager. He played all but the final eight games of his NHL career with the Washington Capitals and was the first goalie in team history to win 300 games.
Though Kolzig was taken by the Capitals in the first round (No. 19) of the 1989 NHL Draft, he was anything but an overnight success. He had brief callups in 1989-90, 1992-93 and 1993-94, and it wasn't until 1996-97 that he went a full season within playing in the minors. Even in 1996-97, he was No. 2 behind Jim Carey and went 8-15 with four ties, though his 2.59 goals-against average for a non-playoff team hinted at better things to come.