There was no true national championship game before the BCS era. However, in 1942 Georgia beat UCLA in the Rose Bowl to earn a share of the National Championship, along with Wisconsin and Ohio State.
For the National Championship, Georgia Southern beat Nevada 36-13 for their 4th Championship Title.
Uconn beat Georgia Tech
The Nebraska cornhuskers beat Florida for the 1995 national championship.
Miami
In 1982 there was no National Championship game. However (#2) Penn State beat (#1) Georgia 27-23 in the Sugar Bowl, Penn state was voted the National Champions in the final regular season poll with a record of 11-1-0
The University of Miami
Alabama beat USC Alabama was the champions
Oklahoma Sooners
North Carolina beat Michigan to win the 1993 NCAA Division I Men's Basketball Championship.
Yes
Duke Blue Devils beat Butler Bulldogs by 2 points to win the 2010 NCAA Men's National Championship