Four: the Pacific, the Atlantic, the Indian, and the Arctic. The existance of a fifth ocean is not established:
"This global, interconnected body of salt water, called the World Ocean, is divided by the continents and archipelagos into the following four bodies, from the largest to the smallest: the Pacific Ocean, the Atlantic Ocean, the Indian Ocean, and the Arctic Ocean, and, according to some authorities such as International Hydrographic Organization(IHO), a fifth ocean, the Southern Ocean.
Some geographers and some governments but not the US, recognize the IHO as defining official water body names and boundaries. (The US authority is the United States Board on Geographic Names.) The IHO officially sanctioned the Southern Ocean name only in 2000, but its definition by a line of latitude (with IHO members widely disputing which line of latitude) has left its acceptance as a fifth ocean open to question. The National Geographic Society and some other leading geographers and cartographers continue to use "South Pacific", "South Atlantic", and "Indian" Ocean for the waters around Antarctica. A few Oceanographers recognize only three oceans also, treating the Arctic Ocean (or the Arctic Sea) as a part of the Atlantic Ocean."