How many world wars have there been?

Assuming that a "world war" is any war that is fought on all the continents other than Antarctica, then there have been Six.

World War 1 aka the War of the Austrian Succession 1740-48

World War 2 aka  the Seven Years War 1754-1763, Known if at all, to residents of the United States, as the French & Indian War.

World War 3  The War of American Independence , 1775-1783, Known  to residents of the United States, as the Revolutionary war, or the War for Independence.

World War 4  The Napoleonic Wars 1803-1815.

World War 5  Commonly referred to as the First World War 1914-1918*

World War 6 Commonly referred to as the Second World War 1937-1945 (i measure from the Japanese invasion of China)*

*I think that if one takes an optimistic view of the future, i.e., that human civilization still includes luxuries like historians to categorize the past :), the common practice in a few hundred years will be not to separate these wars into separate events, not unlike how we consider the Hundred Years War. I would suggest instead:
The War of the German &  Japanese Accessions  1866 - 1989
This period covers the Austrian-Prussian War until the the fall of the Berlin wall.