Are monarchies a recognised form of government within Islam? If not, then how come so many Muslim countries are run by monarchies, usually of a tyrannical nature. 

Islam is less concerned with "who" governs, as opposed by "what standards" government abides. Whether authority is vested in an individual or in a group of people, they should have the confidence of their people, set a good example, and govern in accordance with the principles laid down in the Qur'an. Nobody, ruler or ruled, is above the law. The existing ruling dynasties in Muslim countries are sadly a heritage of the colonial rule where the former occupiers played kingmakers.