A government ruled by a king or queen is called a monarchy. Monarchies are typically associated with hereditary rule, where an individual rules for life and then passes the crown to an heir.
Monarchies are not a prevalent form of government as of 2014. Where they exist, they often take the form of a constitutional monarchy. Under this form of government, the king or queen must share power with elected representatives. In some cases, the monarch is simply a figurehead with no real powers. For example, the monarch of Britain has very limited powers, and the country is actually ruled by Parliament, which is a democratic body.