The 2002 National football champion was THE Ohio State buckeyes. OSU defeated the Miami Hurricanes in a double overtime thriller 31-24 ending Miami's 34 game winning streak.
In 2007, LSU were the BCS National Champions in NCAA Division I FBS football for that respective season. In basketball, Florida won the Final Four for the championship. Oregon State won the College World Series.
The person who provided the answer below shouldn't even be allowed to type. The University of Oregon in fact, won the first NCAA National Championship in basketball in 1939. If you are asking about football and basketball, they have not won any (Incorrect, they won the basketball national title in 1939). However, in cross country and track & field, they have won twelve NCAA championships.
The Florida State Seminoles won the 2014 NCAA football national championship.
Marshall won the Division 1-AA national championship in 1992 and 1996.
NCAA Division I FCS Consensus Mid-Major Football National Championship ended in 2007.
NCAA Division I FCS Consensus Mid-Major Football National Championship was created in 2001.
Alabama won the national BCS championship.