The mighty Incan Empire of South America flourished between 1200 and 1535 AD. They developed drainage systems and canals to expand their crops, and built stone cities atop steep mountains — such as Machu Picchu (above) — without ever inventing the wheel. Despite their vast achievements, the Incan Empire with its 40,000 manned army was no match for 180 Spanish conquistadors armed with advanced weapons and smallpox.