Thompson, a native of Dover, New Hampshire, began swimming for the Seacoast Swimming Association under coach Mike Parratto. She first appeared on the international scene as a 14-year-old in 1987, when she won the 50-meter freestyle and placed third in the 100 m freestyle at the Pan American Games. She won her first world championship in 1991, as part of the USA's winning 4x100 freestyle relay team, and held the world record in the 50 m and 100 m freestyle when she participated in the 1992 Olympics in Barcelona, Spain.

Thought to be at the height of her competitive career at the time, Thompson was expected to win up to five gold medals at those Olympics. However, she failed to qualify for the final in the 50 m freestyle, and finished second in the 100m, where she was beaten by Zhuang Yong of China. Thompson won two gold medals as part of the 4x100m free and 4x100m medley teams. She raised considerable controversy after the 100m freestyle when she commented on the doping policy in Barcelona -- at that time the event winner did not have a mandatory doping test -- only the second and fourth-place finishers were tested, based on a random draw. Thompson thought that Olympic champion should be tested and that rule was changed.

Thompson continued her career as a part of the U.S. team and a member of the Stanford University team, and continued to rank among the world's best swimmers for the next four years. However, a poor performance at the 1996 Olympic Trials kept her from competing in any individual event at that year's Games in Atlanta. She redeemed herself there with three more relay golds, in the 4x100 m freestyle and medley and the 4x200 m freestyle relays.

Between 1997 and 1999, Thompson won eight more world championship titles, including three in a row in the 100 m freestyle, and went to the 2000 Summer Olympics in Sydney, Australia hoping to finally win that elusive individual gold medal. It wasn't meant to be; she won a bronze in the 100 m freestyle and was fifth in the 100 m freestyle butterfly. But in the relay events, she swam the anchor leg in helping the USA defend its titles in the 4x100 m freestyle and the 4x200 m freestyle relays. She also swum the butterfly leg in the winning 4x100 m relays. The 4x100 free and medley teams set new world records in the process.

At the World Championships that year, she broke the world record in the 100 m butterfly for the fourth time, winning a qualifying heat in a time of 56.56 en route to a gold medal in the event.

Thompson seemingly retired from competition after the 2000 season with 10 Olympic medals, eight gold, one silver and one bronze, and 12 gold medals at World Championships. However, she returned to competition the summer of 2002 at the Pan Pacific Swimming Championships in Yokohama, Japan. Thompson won five medals in two days, setting a career-best time in winning the 50 freestyle. At the 2003 World Championships, she would win five medals, including two gold.

At the 2004 Olympics at age 31, she was the anchor member of the 400-meter freestyle relay, she helped set a national record of 3:36.39. However she lost the lead her teammates had built and finished with a silver medal. She gained another silver medal as a member of the 400-meter medley relay, as she would lose another lead that her teammates would give her during the butterfly leg. She would end her Olympic career with twelve medals, the most for any U.S. Olympian in history.

Thompson was the 1993 and 1998 USA Swimming Swimmer of the Year. She ranked as the 62nd greatest female athlete of all time in a 1999 poll conducted by Sports Illustrated. She was named by the Swimming World magazine as the Female World Swimmer of the Year in 1999.