(Great, now I'm all paranoid about double dates and how they're affecting my data...)
Several references have been made to the "double date window", period of time where the Julian and Gregorian calendars overlapped. I can assume the start of the window was at the inauguration of the Gregorian calendar (1582), but when did it end?
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.
The need for dual date representations varied from nation to nation depending upon when they made the transition from a Julian to a Gregorian calendar (and, to a lesser extent, when their trading partners made the transition).
The most comprehensive list I am aware of is posted at http://www.webexhibits.org/calendars/year-countries.html. I cannot vouch for the accuracy of all these claims but it does provide a starting point for checking on particular countries.
Remember also to take account of the impact in their colonies of decisions made in London, Paris or Madrid.
