Contemptible means deserving of contempt or scorn, contemptuous means expressing contempt or scorn toward someone or something, and contumacious means stubborn or willful disobedience toward authority.
The first two words should not be confused: a law-abiding person may be contemptuous of charlatans and con artists and might refer to such characters as contemptible people. The latter two words are more easily confused, though only contumacious concerns disobedience.