Depends on which sport or sports you are asking about.
UCLA - 100 Championships
Stanford with 540
116 national championships since 1895 in football. However most teams don't count their national championship pre ww2!
The UCLA Lady Bruins have won the most National Championships in Collegiate Fastpitch Softball...I believe they have won 25 or 26 National Championships.
MIT?
UCLA
sec
Princeton With 26 National Championships.
UCLA with 11 national championships
The UCLA Bruins :11
Well can we start with Indian River State College in Florida?? Their Men's swimming team has 36 consecutive NJCAA national championships.
Larry Kehres, of Mount Union College, Division III, with 9 national championships.