Can Landlords Discriminate Against Criminal Tenants?

Most people recoil at the idea of discriminating against people and probably just as many presume that existing laws prohibit discrimination. What many do not realize is that the laws against discrimination, for the most part, only cover those in so-called "protected classes." The typical protected classes are, as one may expect, based on race, gender, national origin, religion, age (over 40), and disability. Needless to say, it is unlawful for a landlord to discriminate against prospective tenants on the basis of any of these. Aside from these protected classes, can a landlord discriminate in choosing his or her tenants on the basis of other reasons?