Assuming you mean only the Final Four and not the NCAA Tournament overall, the answer is UCLA.
Depending on which games you choose to include, the number of wins is a constant subject for debate. UCLA has 11 National Championships, the best record of any NCAA school.
One of the arguments over which wins to score stems from the 1980 Championship Game appearance against Louisville. Although the Bruins defeated Purdue (67-62) to reach the finals, the NCAA later vacated the win based upon alleged rules violations. Louisville beat the Bruins to take the National Championship, 59-54.
The other is whether one wishes to count the consolation games which were only played from 1946 to 1981. In those games the losers of each semi-final game played for the third place position. UCLA won twice (2 wins). In 1974 UCLA beat Kansas, and in 1976 UCLA beat Rutgers.
11 National Championships (22 wins in the final four, one win for the semi-final, one win for the National Championship);
2 semi-final wins without a win in the National Championship game (1980, 2006, 2 wins);
2 consolation wins (2 wins);
and the 1980 semi-final win which was later vacated (-1).
Now all you have to do is decide which wins you want to include and do the math.
The "Final Four" are the four teams that win the regional championships in the NCAA basketball tournament, thus becoming the final four teams in the tournament.
By making to the last four teams in the NCAA March Madness tournament
Kentucky has appeared in the NCAA Tournament 50 times and has been to the NCAA Final Four 13 times.
In 2008 this was the first time in the history og Men's NCAA basketball tournment were all four number seeds have had it to the final four. In 2008 for the first time in history of the Men's NCAA basketball tournament all four number one seeds reached the NCAA final four.
The Final Four teams in the 2008 NCAA March Madness tournament were UCLA, Memphis, Kansas, and North Carolina. Kansas went on to win the tournament.
The Final Four is the national semi-final of the NCAA Tournament featuring the winners of the four brackets, which decide who play in the National Championship
Georgia Tech has never won the NCAA Tournament. They were second in 2004 and made it to the Final Four in 1990.
louisville, oklahoma, stanford, uconn.
Through 2013, Kentucky has advanced to the Final Four of the NCAA men's basketball tournament 15 times.