National Invitation Tournament.
Yes. In 1942 West Virginia University won the National Basketball Championship. Although the NCAA might prefer that people forget, in 1942 the NIT was the tournament deciding the National Championship. The NCAA tournament was only 3 years old and teams consistently chose the NIT over the NCAA, as they do the NCAA over the NIT today. WVU finished 16-4 and was one of the 8 teams invited to the NIT, held at Madison Square Garden. They beat Western Kentucky in the final game 47-45 to win the NIT and claim to the National Basketball Championship.
CCNY, led by Irwin Dambrot, won both the NIT and NCAA tournaments in 1950.
No they haven't one a national championship
No. They played in the National Championship once, I think in 1959 vs. California and lost by one point. Actually, WVU won the NIT in 1942. At the time, the NCAA was only 3 years old and the NIT was considered the more prestigious of the two events. Early in the life of the NCAA tournament, teams would turn down invites in favor of the NIT. So while the 1942 team was not the NCAA champion, they were in fact national champions.
Alabama has never lost a national championship game.
WVU played in the 1988 national championship against Notre Dame.
Yes ... Troy won the NAIA national championship in 1968 and the NCAA Division II national championship in 1984 and 1987.
The Maine Bears have never won a National Championship in football.