This is a non-specific question. There are four genuine national champions every year determined through playoff systems. Divisions I-AA, II, III, and NAIA. There is one national champion determined each year through a combination of voting and computer rankings: BCS.
However, if you don't worry about that distinction between championships which are determined by votes and championships which are determined by actual competition on the field, then the answer is Princeton University with 24 championships.
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.
The University of Alabama
The University of Alabama have won the most football national championships with 13
The University of Alabama Crimson Tide have the most national championships in football with twelve.
The University of Michigan has the most with 11 national championships the last in 1997. GO BLUE
Alabama. The University of Alabama has 12 National Championships
In college football Alabama has the most national championships with 13 while Notre Dame comes in second with 12. In College Hockey Bemidji State University has 13 national championships
The Ohio State University has 7 national championships. When they beat the University of Miami in 2002 that gave them their seventh championship since 1952.
Michigan has 11 Football national championships. Go blue!