LSU Men and Women have a combined 64 national championships as of spring 2007. That is, by far, the most by an SEC school.
Arkansas Razorbacks 42 national championships in track
Sidney Stringer Academy
UCLA
DC United
Stanford with 540
UCLA they have 101 national championships in all sports. (11 in basketball)
duke
UCLA
AlAbama
Depends on which sport or sports you are asking about.
ucla
Yale University is the school with the most national championships in football. The school with the most wins in NCAA Division I football is the University of Michigan.