French President Nicolas Sarkozy is a prince of Andorra, this makes him the only democratically elected monarch in the world. The Principality of Andorra is a tiny nation sandwiched in the Pyrenees Mountains between France and Spain.
The principality of Andorra is a tiny landlocked nation in between France and Spain. The nation was created through a 1278 treaty between France and Spain. The treaty was arranged so that there were two co-princes that ruled over the land. One is the Bishop of Urgell, who is of course, appointed by the Pope. The other used to be the Crown of France, which disappeared with the French Revolution and gave way to the French Republic.
This unique arrangement means that the president of France is the only democratically elected monarch. Despite this, though, he's not elected by his subjects. The president is elected by the French and not by the Andorrans.