How many continents are not connected to any other continent?

Australia and Antarctica are the only continents that have no land connection to another continent.

If you count Europe and Asia as two separate continents then they are two connected continents, and North America and South America are connected by way of Central America, leaving Africa, Australia, and Antarctica as the continents that are not connected to other continents. Sometimes we consider Europe and Asia to be a single very large continent called Eurasia.