Democratically Elected Leaders
Since spreading freedom and democracy would seem to be the newest hobby of the current American administration, a few notes of explanation are in order.
There are very few democratically elected world leaders. The leaders of most "democratic" countries are not, themselves, elected by their people. Prime ministers are the leaders of political parties. Most of the European leaders were selected in the same manner as Tom DeLay: they are the majority leader of the largest party in the lower house of a parliament.
The presidents of France, Russia, the Palestinians, Iran, Malaysia, Mexico, and a few other countries are actually democratically elected, which is to say they are elected by a direct vote of the people of their countries. The President of the US is not a true democratically elected official because of the electoral college.
In many countries voters actually choose parties, not candidates. The parties have a list of candidates usually equal to the total number of seats in their parliament. After the election the party learns how many seats it has won based on its percentage of the vote and people take office based on their position on the list. This is the system used in Iraq's recent election.
Even "democratic" countries can have less than democratic features: the military in Turkey heavily influences government actions, as does the Iranian council of clerics, and some in the US would claim the Supreme Court does the same thing.