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 Dayton Flyers have not won a National Championship in any men's or women's sports.
I wouldn't say 'national championship' but the professional sport of frisbee is 'ultimate frisbee'.
Mississippi State has not won a National Championship.
University of Texas
The motto of Korea National Sport University is 'Truth, Sacrifice, Creation'.
Australia established its national first class championship in 1892-93
Wrestling is the sport in Oklahoma.
Oklahoma state universtiy
The Oklahoma Sooners? Football, of course!
I believe Pitt and Ole Miss have never won a national championship. Update: Ole Miss actually has won a national championship in Tennis but not football.