In comments on another question, System Down says "the rest of the Muslims believe that Mirza Ghulam Ahmad's claims are false, and that he is a false claimant to prophethood" and links to a table in Wikipedia.
I'd like to hear a more thorough answer. Why do Sunni Muslims consider Ahmadiyya beliefs false, and why do they consider the aberrations so severe that they exclude them from even being called Muslims?