Core countries are the industrialized countries on which other non-core countries depend. Core countries (illustrated in blue in the figure) control and benefit from the global market. They are usually recognized as wealthy nations.

Core countries do not always stay core permanently.  Before 16th century, Asian and Middle Eastern empires were considered as core. Today, core nations are generally the most developed countries.
Based on Babones and Alvarez-Rivadulla (2007), current core countries (based on alphabetical order) are Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Iceland,  Ireland,  Israel,  Italy, Japan, Luxembourg, Netherlands, New Zealand,  Norway,  Singapore, Spain, Sweden,  Switzerland,  United Kingdom and United States.
In order for a country to be considered a core country nominee, the country must possess an independent, stable government and potential for growth in the global market and advances in technology.

Source: Wikipedia