There were numerous consequences of the Age of Exploration and Expansion of Europe; however the greatest are probably the expansion of Western European influence and culture and also the Colombian Exchange.
Because of its Christian/Aryan culture, Western Europeans considered themselves superior to those of other races and ethnic groups. Additionally, because of the close geographic proximity of western European nations to each other and the poor relations that existed between them, Europeans soon developed weapons superior to those of the rest of the world. Although developed for use against other Western nations, these weapons meant that American and Asian people were no match for European forces. This augmented the feeling of Western European superiority. Europeans in Asia came not to cooperate but to trade on their own terms, and, if possible, to dominate and Christianize. Vasco da Gama told the Indian pasha that he came for "Christians and spices." When the Indians were unwilling to cooperate at first, Da Game seized a fishing boat, dismembered its crew, and sent their body parts back in a basket as a warning against failure to cooperate. It is this type European domination which has led Western languages, clothing and customs to dominate much of the world.
A greater influence, perhaps was the Columbian exchange between the Americas and Europe. Plants such as wheat and oats travelled to the Americas while maize (corn), pumpkins, squash and potatoes travelled to Europe. Additionally, sheep, cattle and horses travelled to the Americas and turkeys travelled to Europe. Sadly, diseases, primarily measles, mumps and smallpox travelled to the Americas with devastating effect. Charles Mann's 1493 provides an excellent discussion of the Columbian Exchange.