America has traditionally had one of the most successful Olympic gymnastic teams. The woman with the most Olympic medals is Larissa Latynina.
Michael Phelps
Ole Einar Bjørndalen has won the most Winter Olympic medal with 13 total medals. The American with the most Winter Olympic medals is Apolo Anton Ohno with 8 total medals.
Michael Phelps the American swimmer
The most gold medals won by an American women in the Winter Olympics is 5 by Bonnie Blair.
Carl Lewis
Bonnie Blair
As of the 2008 Games that would be Jenny Thompson who won 12 Olympic medals (8 gold, 3 silver, 1 bronze) in the 1992, 1996, 2000, and 2004 Games.
As of yesterday August 8, 2008, Mark Spitz owns the most Olympic GOLD medals for swimming in a singe Olympic Games. Seven in the Munich 1972 Olympic Games. The Question was about the most Olympic medals owned by an United States swimmer so that might not be the answer sought.
Jenny Thompson
Ole Einar Bjørndalen has won the most Winter Olympic medal with 13 total medals. The American with the most Winter Olympic medals is Apolo Anton Ohno with 8 total medals.
Michael Phelps won the most with 14.