When did Jack Sparrow do his deeds?

Answer 1

Although the Pirates movies are not entirely historically accurate, the events, places, and status of characters generally suggests that the movies occur some time between 1720-1750.

The main reason for this conjecture is that "Golden Age of Pirates" is generally considered to be from about 1690-1730. In the second film, Beckett says "Jack Sparrow is a dying breed. The World is shrinking. The blank edges of the Map filled in. Jack must find his place in the new world or perish." You can even see the mapmaker fill in the map in Beckett's office throughout the course of the three films, and the huge wall map is especially prominent in Dead Man's Chest. By the end of the 1600s, colonization was growing rapidly in the Americas, and piracy was beginning to die out. Since piracy is having its last hurrah during the POTC trilogy, we can therefore assume that the films take place some time in the floating 30-year period after the Golden Age of Pirates.