1. The Chinese Empire ranging from the Qin Dynasty, Han Dynasty, Sui Dynasty, Song Dynasty, Ming Dynasty to the Qing Dynasty. China throughout world history have been the center of civilization and enjoyes the longest continous civilization. Their influence with their major inventions such as gun powder, printing press, the fire lance, land mine, naval mine, hand cannon, exploding cannonballs, waterwheels, paper, compass, and carriage wheels changed the world upside down. 50% of the world's populace is within the sphere of Chinese influence, and through their achievements, many cultures have adopted the Chinese way of life, that changed the composite Indian, Far Eastern, Middle East, and Europe's civilizations.
Note: the most spoken language in the world is Mandarin Chinese, greatly dwarfing English, Spanish, or Hindi.
2. Greek Empire/Roman Empire (tied) in my opinion truly did not have an empire that is vast in territorial expansion. However, its philosophical and cultural legacy is vivid throughout Europe and all over the world. The reign of power by Alexander the Great (Macedonian with Greek culture) during the Hellenestic era and the defeat of the Persian Empire help diffused the Greek culture throughout much of the known world, expanding as far as India. Today, the Greek culture of egalitarianism, democracy, political autonomy, and popular sovereignty have contributed to the legacy of world political system. The Roman Empire which failed to conquer Germania early concentrated on defeating the Franks, Visigoths, etc, and successfully created one of the greatest empire in history. Their urban patterns is still reflected in many of today's societies such as the aquaducts and grid pattern roads and highways. With its division with the Byzantine, the territorial legacy of the Roman Empire crumbles but the remnants of their culture never ceased to expand.
3. Mongol Empire- The largest continous empire in history. Massacred 70% of Persians, sacked Baghdad and burned it to the ground, kills almost every living inhabitants of Kiev, paralyzed the Ottoman Empire, shattered Russia and Central Asia, pounded China and Korea, destroys Poland, Hungary, and humiliates the Russ Viking descendants of the East and eat every Teutonic Knight for dinner. A barbarian empire that made the most sense of the Dark Ages. Their reputation is so influential that Europe began to shake in fear and knew their technological inferiority needed to be address as the major issue. Marco Polo's visit to the superior empire of the Middle East, Central Asia via Silk Road to China, brought him new ideas of wealth outside Europe. The Mongol Empire had an indirect influence to the European exploration after Marco Polo discovers the inferiority of Europe compare to the empires sacked by the Mongols.
4. Umayyad Dyanst (Middle East) There was once in a long time that the Sunnis and Shias were together as one. From the legacy of the Great Prophet Muhammad, Muslim warriors from Saudi Arabia, Syria, and Palestine goes out in an all out war with the Persians, Central Asians, crosses the Caucausus Mountains, invades North Africa, conques Iberia, atacks Sicily and Southern France, and dominated the Medditerranean Sea for centuries. The Umayyads legacy also provided Muslims to expand Islam through Africa, India, China (Western China have over 30 million Muslims, there are more Chinese muslims than Saudi Arabians or Iraqis), and Southeast Asia.
5. Britain- The underdog British shocked the world with its victory against the favorite, Spain, considered as the most powerful country in the world throughout the early to latter 1500s. With Spain's defeat, Britain was now free to explore anywhere without the fear of Spanish intimidation. Britain conquers North America, parts of Latin America (Belize & Carribean portions), conquers parts of Southeas Asia, India and Pakistan, Africa, Australia and NZ, and other Pacific Islands. The British legacy is not mere based on the English cultural expansion but the diffusion of the Industrial Revolution that led to mass production.
Empires that could have easily made it: Persia, Spanish and India(Mauryan and Gupta).
Note: French, Dutch, Portuguese, Americans, Russians, Suri Vaja (Southeast Asia), Japanese, Germans, have been great empires but nowhere near close to the legacy these top 5 empires have done in history.
