As of 2014, Barack Obama is the president of Puerto Rico. Puerto Rico is a territory of the United States, so the president is whoever is currently the President of the United States.
Puerto Rico also has a governor whose position is analogous to that of the governor of one of the United States. He holds executive power over the territory. As of 2014, Alejandro Garcia Padilla is the Governor of Puerto Rico. Although citizens of Puerto Rico do vote to elect their governor, they cannot vote in U.S. presidential elections. They may, however, vote in the primaries to select a party's nominee for that office.