Mayor is a word that specifically means the leader of a town. Chief means the leader of a tribe. Governor means the leader of a state or province. Words like Emperor or King imply the head of a country. What word would imply like these that someone is the leader of a planet?
Obviously, we haven't had one (yet), so there's not a canonical word like "Mayor" is for cities. The Secretary-General of the United Nations, Ban Ki-moon, could not be described with this word because he is not the head of state of Earth. Imagine if we had a global election and chose one leader of Earth. This term would describe that person after he took office.
There are plenty of terms that could be used if such a situation would actually happen. President, Chancellor, Prime Minister, and words like this could be used, but they serve more to imply how the person was given their authority. Even King and Emperor would fall into this category, as having a head of state imply that the planet is now one huge nation. None of these terms, however, specifically imply that this leader is installed at the planetary level.
City :: Mayor as Planet :: what?