Looks like the commonly described "Golden Age of Piracy" spans from the mid 17th to mid 18th century, from a quick search. During this period the major powers were the Portuguese, the Spanish, the Dutch and the English.

Global power in this time period can be examined in terms of influence in two main areas - the Americas and the Indian Ocean; sometimes referred to as the West Indies and East Indies.

In the Indian ocean region, power was firmly in the hands of the Dutch, Portuguese and English. This was primarily due to the significant economic power they held in the region rather than any actual territorial control. The Dutch and English trading companies (The VOC and the East India Company respectively) had been granted significant authority to carry out affairs of state, which included diplomacy and warfare. By this period, the power of the Portuguese was decreasing as they were outcompeted by the Dutch and the English, but it was still significant nevertheless.

In the Americas, Spanish control was much more significant. They had been working on their colonisation of the islands of the Caribbean and the mainland since the arrival of Columbus in 1492, so they had established a significant foothold. The portuguese were also active in this area, mainly in South America. This is a rough map of the areas of controlled by each country in 1648.

These new world powers replaced a number of older ones:

• The Chinese after the during the decline of the Ming Dynasty had ceased sending out their treasure fleets to demand tribute from other rulers. This left a void in the Indian Ocean trading region which was exploited by Europeans new to the area.
• The Ottomans declined in the late 17th century; this was a fairly complex topic in itself but a significant factor was the stagnation of innovation in the empire, contrasted against rapid technological developments in Europe which placed them at a disadvantage.

If you're interested in the Indian Ocean and the trade and interactions that went on there, you might like to read "Trade and civilisation in the Indian Ocean: an economic history from the rise of Islam to 1750" by K.N. Chaudhuri.

This is my first attempt at an answer on here, any feedback is greatly appreciated!