After not getting invitations to the NCAA Tournament or the NIT, the following basketball programs have all declined a bid to play in the lesser CBI tournament (and for that matter, the bottom-of-the-barrel CIT).

Florida Gators (16-17) [yes, these tournaments will take teams with losing records.]
Tennessee Vols (16-16)
South Carolina Gamecocks (17-16)
Clemson Tigers (16-15)
Florida State Seminoles (17-16)
Oregon State Beavers (17-14)
Cal Golden Bears (18-15)
TCU Horned Frogs (18-15)
Penn State Nittany Lions (18-16)
Memphis Tigers (18-14)
Northwestern Wildcats (15-17)

Even the Princeton Tigers (16-14), the Toledo Rockets (20-13), and the Akron Zips (21-14) declined. There are others of note I am sure.

The Colorado Buffaloes (15-17) are the only major program to accept a CBI invite.

If you care to see the CBI schedule, you can see it here. The red-headed stepchild CIT is here. New Jersey Tech, y'all!