As of 2009, 22 NCAA tournament appearances. 3 elite 8 appearances prior to the 2009 tournament.
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.
John Wooden
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.
Missouri has never won an NCAA championship.
15
None. Their best showings were Final Four appearances in 1943, 1947 and 2003.
Michigan State has had 22 NCAA Tourney appearances. They curently sit 28th on the the all-time list.
Washington
They have 38 NCAA Tourney appearances at this time
BYU or Missouri -- it's one of them. I'm pretty sure it is Boston College. 18 tournament appearances, 22 wins, no final fours.
NC State has made 3 NCAA Final Four appearances (1950, 1974, 1983).