In addition to the 1942 and 1980 seasons:

"The 1920 NCAA football season had no clear-cut champion, with the Official NCAA Division I Football Records Book listing California, Georgia, Harvard, Notre Dame, and Princeton as national champions."

Moreover, the 1927 NCAA football season had no clear-cut champion, with the Official NCAA Division I Football Records Book listing Georgia, Illinois, Notre Dame, Texas A&M, and Yale as national champions.

Furthermore, the 1946 NCAA football season had no clear-cut champion, with the Official NCAA Division I Football Records Book listing Army, Georgia, and Notre Dame as national champions.

Finally, the 1968 NCAA football season had no clear-cut champion, with the Official NCAA Division I Football Records Book listing Georgia, Ohio State, and Texas as national champions.

http://grfx.cstv.com/photos/schools/aub/sports/m-footbl/auto_pdf/2013-14/misc_non_event/20140421_ncaa_champions.pdf

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Note: in 1983 Alabama Football claimed the 1941 national championship despite a 9-2 record with shutout losses to Mississippi State and Vanderbilt, and finishing the season ranked #20 in the AP Poll:

http://bryantmuseum.com/champs.asp