Countries ruled by Emperors are Empires.
Currently there is only one Emperor in the world and it's
Emperor Akihito of Japan (which isn't technically an Empire!)
Past countries ruled by an emperor were:
Roman Empire (Augustus was the worlds first emperor)
Byzantine Empire
Persian Empire
Ottoman Empire
Holy Roman Empire
Austrian Empire
Bulgarian Empire
Serbian Empire
Aztec Empire
Inca Empire
Russian Empire
French Empire (Napoleon)
British Empire (although the emperor usually called sovereign or
king/queen)
German Empire
Spanish Empire
Chinese Empire
Japanese Empire
Korean Empire
Mongolian Empire
Vietnamese Empire
Brazilian Empire
Ethiopian Empire
Somalian Empire
Central-African Empire