"Olie the Goalie" has been a part of the Washington Capitals franchise since being selected by them in the 1989 Draft. He spent several years in the American Hockey League with the Baltimore Skipjacks, the Hampton Roads Admirals and the Portland Pirates, after playing major junior hockey for the New Westminster Bruins and Tri-City Americans of the WHL. During Kölzig's time with the Americans, he had an on-ice fistfight with Portland Winter Hawks goaltender Byron Dafoe, someone with whom he would go on to have a friendly rivalry in the NHL. On November 29, 1989, Kölzig scored a goal with the Americans.

Olaf played his first NHL game in the 1989-90 NHL season, only to be sent down to the minors for a few years. In the 1995-96 NHL season, he was brought up to be a backup for Jim Carey, replaced him the season after, and has been the starting goalie ever since. Kölzig holds virtually every Capitals team record at his position.

In the 1997-98 season Kölzig lead the Capitals to the Stanley Cup Finals. In the playoffs, he became only the tenth goalie in NHL history to record four shutouts in one postseason. The Caps were swept in four games by the Detroit Red Wings.

In 2000, he won the Vezina Trophy as the NHL's best goalie after going 41-20-11 with a 2.24 GAA and five shutouts. In the American Hockey League he won the 1994 Jack A. Butterfield Trophy (MVP of the American Hockey League playoffs) and the 1994 Hap Holmes Memorial Award.

He was also the starting goalie for the German Olympic team in the 1998 Winter Olympics in Nagano, Japan, recording a 1.00 GAA and went 2-0. He also played with the German team in the 2004 World Cup, yet went 0-3 with a 3.34 GAA. Kölzig also has the distinction of being one of four goaltenders to play a scoreless period during an NHL All-Star Game, having done so at the 2000 All-Star Game. He also played in the 1998 All-Star Game, in which he made 14 saves on 17 shots.

In recent years, Kölzig's numbers have taken a dip due to his age and the Capitals less-than-stellar defense. He is not the marathon man he once was, averaging 68 games and 4,000+ minutes a season. As part of the Capitals' youth rebuilding effort and Kölzig's age, he plays fewer games and sees himself splitting time with backup Brent Johnson. Through 63 games of the 2005-06 season, he has played 48 games.

In 2004, the Capitals held a vote for fans to determine the top 30 players in the franchise history to celebrate their 30th season in the league. Kölzig's 2,038 votes led all players.

In 2005, he and fellow Tri-City American alumni Stu Barnes became part of an ownership group in their former major junior team, assuring the existence of the Americans in Kennewick, Washington for about ten years.

Kölzig also started in goal again for Germany's Olympic team at the 2006 Winter Olympics in Turin, Italy.

On February 11th 2006, Kölzig signed a two-year, $10.9 million dollar extention with the Capitals.