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NCAA Division 1 Mens Basketball championship
I wouldn't say 'national championship' but the professional sport of frisbee is 'ultimate frisbee'.
Bowl Championship Series
Mississippi State has not won a National Championship.
The University of Oklahoma did not win any national championships in 2010. The last time a sport at the university won a national championship was the 2008 gymnastics team.
The college football national championship is the highest team award in the sport. The Fighting Irish of Notre Dame has won the most championships in history.
University of Texas
Men's Division I College Football.
Australia established its national first class championship in 1892-93
The Dayton Flyers have not won a National Championship in any men's or women's sports.
The NCAA record is 31 consecutive national championships, 1980 to 2010, in Men's Swimming & Diving, Division III, by Kenyon College (Gambier, Ohio). This was the longest streak in any division in any sport in NCAA history.The NCAA record for most total championships in any one sport is the same - Kenyon College - Men's Swimming & Diving - 31 total NCAA national championships.