What college football team has won the most National Championships?

Yale with 18, although their last one was in 1927.

1927 - Yale Claimed National Title -- Yale won its record 18th national championship. However, 1927 is the last time the Bulldogs were crowned National Champions.
1922 - Princeton Grabbed Title - Ivy League power Princeton claimed its 17th National Championship. However, it was the last title for the New-Jersey based school. Currently, Princeton is second with 17 National Football Championships.

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http://football-advance.blogspot.com.au/2007/01/historycollegiate-game.html

Who has won the most NCAA college football national championships? --- The college football national championship was determined by sportswriters beginning in 1936. The national champion has been determined by computer selection leading to a bowl game playoff since 1998. The most national championships won by one team since 1936...Oklahoma and Notre Dame, each with 7.

http://www.cloudcroft.com/news/news132.htm

Princeton has the most with 24 recognized championships. But since 1936 Notre Dame sits on the hill with 12. Check it out at https://en.wikipedia.org/wiki/NCAA_Division_I-A_national_football_championship#1869-present