One that I can mention is the Spanish War of Succession (1701 - 1714), which is considered to have a global affect.

The fighting happened both at land and at sea in Europe, all over Europe. Some powers that I can name that were fighting each other were; Great Britain, France, Spain, Portugal, Prussia, Austria, England, Scotland, the Dutch Republic, the Holy Roman Empire. Most of them fought on land, while the others such as England, Spain, France, and the Dutch, were able to use their navies against each other (notable ones are Great Britain taking Gibraltar and the Anglo-Dutch fleet that attacked San Roque in Spain).

This war reached across the Atlantic and spread across the North American colonies and (some of) the Caribbean (from Newfoundland, down the Eastern Seaboard, all the way to the Eastern islands in the Carribean such as St. Kitts. for example). The North American theatre of the Spanish War of Succession is called the Queen Anne's War. Britain and France fought for control across the North American colonies (which would later lead to the Seven Year's War).

Britain, Spain and France had their navies in the West Indies. British ships were sent from Jamaica to fight French ships near Saint Domingue, while islands like Cuba and Jamaica remained largely unscathed from military campaigns. IIRC the Portuguese and Dutch also had ships, but weren't really involved in the Carribean theatre where Britain, Spain and France were at. I remember from someone else's comment that the Portuguese had some naval presence by Brazil, while the Dutch owned the islands of Aruba and Curacao.