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.
Notre Dame, with 13 National Championships 11 of which are outright.
The University of Alabama
The University of Michigan has the most with 11 national championships the last in 1997. GO BLUE
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.
116 national championships since 1895 in football. However most teams don't count their national championship pre ww2!
quarter back of course
Alabama has 12 national championships, and 53 bowl appearances, both NCAA records.