Stanford won 6 team championships in 1992 (women's basketball, men's gymnastics, mens swimming/diving, women's swimming/diving, men's tennis, women's volleyball).
UCLA has won the most consecutive NCAA Division I Men's basketball championships, but Kenyon Univ has the most consecutive championships in any sport with 30 in DIII Swimming and Diving. Hobart College has the most consecutive team championships in any sport with 12 in D III Lacrosse.
Michael Phelps has won 33 medals in the World Championships for his sport, Swimming.
UCLA - 100 Championships
UCLA with 11 championships since 1920.
UCLA
slippery rock
Arkansas
12
Alabama
duke
LSU Men and Women have a combined 64 national championships as of spring 2007. That is, by far, the most by an SEC school.