Richter's involvement with the United States national program began when he played in the World Junior Championship in 1985. He was chosen for his standout play at Northwood Prep high school, a Lake Placid school known for its hockey teams.
Two weeks after his high school graduation, the New York Rangers chose Richter in the second round of the NHL Entry Draft. Richter had decided to attend the University of Wisconsin, made the league's Second All-Star Team the following year and then left school to join the United States national team in preparation for the 1988 Olympics. He played for the team for a year and a half, including the 1987 World Championship, and was the starting goalie in four games for the U.S. at the Calgary Winter Olympics in February 1988.
Richter made his first appearance for the Rangers in the 1989 playoffs, but only after playing a full season with the Colorado Rangers in the IHL and despite winning an award as the most outstanding player at the New York training camp in 1988-89. His one playoff game was followed in 1989-90 by a season split between the Flint Spirits of the IHL and the Rangers. Richter joined New York full-time in 1990-91 and shared the netminding duties with John Vanbiesbrouck. The two goalies made a formidable pair and neither was considered the default number one choice. In his second full year in the league, Richter was a finalist for the Vezina Trophy as the league's top goalie, and he posted his third consecutive winning season in 1991-92.
In 1992-93, Richter struggled, slumping to a 4.21 goals-against average in his first 22 games. When Vanbiesbrouck was traded to the Florida Panthers the following summer, the focus of number one goalie shifted to Richter. He responded with some of the best play of his life. By early 1993-94, it became apparent that he was a different kind of goaltender and the Rangers were a different kind of team.
His standout performance in the first half of the season earned Richter a chance to play in the 1994 All-Star Game, a high-scoring contest held at his home rink of Madison Square Garden. Richter was selected as the most valuable player, the first goalie to garner that honor since Grant Fuhr in 1986.
Richter and the Rangers maintained their torrid pace in the second half of the season. With his career-high fifth shutout in a 3-0 win over the New Jersey Devils, Richter surpassed Eddie Giacomin's Ranger record for most wins in a season with 38. Richter finished the season with 41 wins and the Rangers won the Presidents' Trophy as the top regular-season team. Richter's winning hand continued into the playoffs. He had four more shutouts and won all 16 games as New York won its first Stanley Cup since 1942.
In 1996 Richter was once again a primary reason for his team's championship run, this time representing the United States at the World Cup. In the final game of the tournament, an incredible contest against goalie Curtis Joseph and the Canadians in Montreal, Richter faced a barrage of shots and kept his team alive. When the U.S. rallied in the third period to win the game and the title, Richter was selected as the World Cup's most valuable player.
A member of the 1998 U.S Olympic team in Nagano, Richter was selected later that summer by the Nashville Predators in the Expansion Draft, but it was a temporary move. Upon being selected by the Predators, Richter was re-signed by the Rangers less than a month later. Used to playing a minimum 60 games during the regular season, Richter would be plagued by injuries in 2000-01 and over the next three seasons. After representing his homeland for a third time at the 2002 Olympic Games in Salt Lake City, Richter would dress for only 15 games during the 2002-03 season due to injury and subsequently retired from the game in September, 2003.