Michigan State has the most final 4 appearances
either Roy Williams or Dean Smith
UCLA with 10, Cincinnati and Duke with 5
Including the 2012 NCAA Tournament: Brigham Young University has made the Tournament 28 times and has never made it to the Final Four. Missouri is second, with 26 appearances without ever making the Final Four. Xavier, which so far has won in the 2012 tournament as this is being written, is third with 22 years without an appearance.
Brigham Young University has made 22 NCAA Tournament appearances without advancing to the final four. This is as of the end of the 2007 season.
North Carolina has 18 Final Four appearances. 1946, 1957, 1967, 1968, 1969, 1972, 1977, 1981, 1982, 1991, 1993, 1995, 1997, 1998, 2000, 2005, 2008, 2009
With the victory over Xavier in 2008, UCLA has 18 Final Four appearances. If North Carolina wins, they will notch their 17th appearnce.