The Republic of Bou Regreg

This sounds like something out of history mad-libs: In 1627, a Dutch convert to Islam lead a group of Moroccan pirates from his personal city state to the shores of Iceland to seek plunder and slaves.

The man in question is Jan Janszoon.  He started his career as a privateer, authorized by the Dutch crown to attack Spanish shipping.  After being captured by North African pirates in 1618, he converted to Islam (possibly at gunpoint, or possibly because the pirate crew made some very insightful theological arguments) and joined their crew.  After his captain was killed in battle the next year, he took control of the city of Salé on the Moroccan coast.  Although nominally under the control of the Sultan of Morocco, the city was essentially a self-governing pirate lair.  Jan (by then called Murat Reis) was elected their Grand Admiral, a position more commonly known as "Pirate King".  

Using the Republic of Salé (also known as the Republic of Bou Regreg, a way better name) as his base of operations, he raided the shipping throughout the Mediterranean, as well as up the Atlantic Coast to England and Ireland.   In 1627, he took a captured Danish sailor as his guide to Iceland, where he and his band of Moroccan pirates came upon the peaceful fishing village of Grindavík.  As it turns out, peaceful Icelandic fishing villages are not rich with plunder, so the pirates decided to abscond with a few local families instead.  

The Icelanders were sold into slavery back in North Africa, but a few of them were eventually rescued and returned to Iceland.  For his part, Jan was eventually captured by the Knights of Malta, and imprisoned and tortured in their dungeons for five years.  After his rescue by Tunisian corsairs, he returned to Morocco to a hero's welcome, and was granted governorship of a lavish fortress.

Knights of the Caribbean

The Knights Hospitaller were founded way back in 1099 to run a hospital (thus the name) in Jerusalem to provide medical care for pilgrims.  As is true in both video games and real life, being the medic all the time gets boring, so they started providing armed escorts for pilgrims as well.  They distinguished themselves in battle, and built a bunch of pretty badass castles throughout the Holy Land.

After the crusades turned for the worse, and the Holy Land was lost, they retreated to Cyprus, and then took the island of Rhodes from the Byzantines in 1309.  They held out in Rhodes even after the Ottomans had conquered the region including Constantinople, but were eventually flushed out by a an invasion of hundreds of thousands of Ottoman soldiers - and even then it took the Ottomans half a year to dislodge the 7,000 knights.

They then moved on to Malta (apparently they had a thing for island fortresses), where they started protecting Christian shipping in the Mediterranean from the Muslims.  Protecting soon turned to plundering, and the Knights started capturing and looting Muslim trade ships.  This practice brought in huge amounts of money to the otherwise struggling order.

In the mid 1600s, the Knights of Malta became one of the most unlikely colonial powers when they acquired a set of islands in the Caribbean.  Phillippe de Longvilliers de Poincy arrived in St. Kitts in 1638 under the pretense of governing on behalf of the French crown.  He quickly decided that he wasn't nobodies bitch, and started governing under his own authority, as well as capturing other islands in the area.  He took Tortuga (a small island off the coast of Haiti) as well as St. Croix, St. Bart, and St. Martin.

In addition to his other duties of establishing personal island kingdoms, de Poincy was also a high-ranking member of the Knights.  He persuaded them to purchase some of his islands for 120,000 livres (which is a lot, apparently).  The French were willing to accept the governance of the Knights, on the grounds that they should use the islands as a base to protect Christian shipping, and work for the "conversion of the savages".

The possessions of the Knights didn't last long, as they were quickly gobbled up by the likes of Spain and Britain.  Even so, the Knights earned the right to count themselves among the great European colonial powers.