The University of Texas has made the Final Four three times: 2003, 1947, 1943 They have yet to win the national championship in Division I basketball.
Penn State never won the national championship but they've made the final four several times.
The University of Houston and the University of Illinois have both been in the Final Four 5 times. Neither of them have won a championship.
5 Times
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No. They went to the final with him in his Freshman and Sophmore year but lost both times. After his sophmore year, he went pro.
Texas Longhorns Men's Basketball28 NCAA Tournament Appearances 13 Sweet Sixteen Appearances7 Elite Eight Appearances3 Final Four Appearances0 National Championship AppearancesTexas Longhorns Women's Basketball23 NCAA Tournament Appearances 12 Sweet Sixteen Appearances8 Elite Eight Appearances3 Final Four Appearances1 National Championship Appearance (won, 1985-1986 season)
UCLA, eleven times.
In men's basketball, Kentucky has more NCAA basketball championships. Kansas' men's basketball team has won the NCAA championship three times while Kentucky's men's basketball team has won the NCAA championship eight times. In women's basketball, neither team has a championship.
The Wildcats men's basketball team of Villanova University has won a single NCAA championship, in 1985. The team has to date been in the tourney 33 times and has made the final four eight of those times.
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Georgetown has made the final four 5 times: 2007, 1985, 1984, 1982, 1943 Georgetown lost the championship game in 1943, 1982, and 1985. They lost in the semifinal game in 2007. They won the championship in 1984.