Cornell has never won the NCAA Men's Basketball Championship. They made it to the Sweet Sixteen in 2010, losing to Kentucky, 62-45.
Princeton hasn't won a game in the NCAA tournament since 1998 when they beat UNLV in the first round, 69-57.
2 -- Cornell and Syracuse
There was no 1933 NCAA Tournament. The first NCAA Tournament was in 1939 with Oregon beating Ohio State in the Finals.
Kansas
Michigan was a #3 seed when they won the NCAA Men's Basketball Tournament in 1989.
Kentucky
The Ivy League has never produced an NCAA tournament champion. However, if you just mean a game won by an Ivy League team, the most recent was in 2010 when Cornell beat Wisconsin, 87-69 in the second round.
Syracuse
Indiana
Kansas
UCLA
They have made it to the tournament 43 times. And they have won 11 of the NCAA tournament championships.