The cornhuskers
SEC
The answer to this question is tricky. There are several different 'titles' that have been won since universities began competing in sports. There are NCAA titles which go back several decades (sorry, I do not know the history of the NCAA, but they have a website: ncaa.com). The NCAA gives out 'titles' to teams and to individuals. There have been other institutions before the NCAA that gave out 'titles' to universities. The only definitive answer that I know of, is based on NCAA team titles. UCLA has won 104 team titles with Stanford and USC in second and third with fifteen-to-twenty less team titles.
The Alabama Crimson Tide have won the most NCAA Football Titles The UCLA Bruins have won the most NCAA Basketball Titles The USC Trojans have won the most NCAA Baseball Titles In Women's NCAA Basketball the Connecticut Lady Huskies have the most NCAA Basketball Titles
The University has seven titles recognized by the NCAA.
ALABAMA has 12
Five.
In Football it is Princeton with 28 titles. In Basketball it is UCLA with 11 titles.
The University of Oklahoma has won 7 undisputed NCAA Football Championships.
Texas
yes
Sport is called Athletics in colleges, universities and university-preporatory schools. There are many subsets of athletics, including varsity athletics and College Football.