The Gregorian calendar was accepted at many different times by countries around the world, the last accepting it in the 20th century. A list of countries and dates can be found via Google. Catholic countries accepted the change immediately, since it was a papal edict; protestant and non-Christian countries were reluctant (polite way of saying violently opposed) to obeying the Roman church. They straggled along, converting when the practical advantages became great enough.
Of most importance to genealogists in the English speaking world, the United Kingdom and its colonies made the change in 1752, when the second of September was followed by the 14th of September.