One major interaction that comes to mind is the Crusades period from 1095 - 1204. Today, our world sees many violent clashes between fundamentalist Islamic societies and traditionally Christian Western governments. Much of this animosity can be traced to the Crusades, where we first see a major schism between Christians and non-Christians, which eventually led to the cultural animosity we see today. Additionally, this period set the stage for the Middle East to be a hotbed of religiously motivated violence as various groups competed to gain control of the "holy land."
The Crusades also helped develop a global economy. As Crusaders form Europe explored eastern lands, they returned home with spices, fabrics, foods, etc. that no one in Europe had seen before. This led to a greater demand from trade with Asia. Such demand was furthered by the travels, and subsequent writings, of Marco Polo, who spent years within the Mongol Empire. In fact, the Pax Mongolica created by this powerful empire helped bring about a global trade system as travel along this Silk Road was secured. Today, trade is ubiquitous across our globe, and such economic patterns can be traced back to this early period.
Moving forward, another important event that forever changed our world was Columbus's "discovery" or the western hemisphere in 1492. The obvious consequence of this discovery is the colonization of North and South America, which in turn led to many of the nations in existence today. However, there were other effects as well. For example, Columbus’s treatment of the native Taino people he encountered set a precedent for European interactions with natives. Europeans began to see themselves as superior, and subsequently sought to dominate other civilizations. This continues today with the plight of minority ethnic groups who face the destruction of their homelands.