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.
With the victory over Xavier in 2008, UCLA has 18 Final Four appearances. If North Carolina wins, they will notch their 17th appearnce.
Technically, UCLA and North Carolina have each reached the Final Four of the NCAA men's basketball tournament 18 times-- through 2013. However, UCLA was forced to vacate its 1980 Final Four participation due to infraction stemming from the use of ineligible players. Thus, the NCAA credits UCLA with only 17Final Four appearances.
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.
Cardiff, with two.