I believe that Alexander the Great does deserve his reputation. Alexander not only carved out a large empire through the military conquest of powerful nations, he also brought Hellenic cultural values to his conquered territories. Alexander's accomplishments become even more impressive when one considers the fact that he only lived to be 32 years old.
Militarily, Alexander the Great famously conquered the powerful Persian Empire after he established control in Greece. During the conflict with Persia, Alexanders armies never were defeated, a significant fact because of the power of the Persian Empire at the time.
The empire created by Alexander the Great consisted of over 2,000,000 square miles of territory. Alexander is also credited with the development of approximately seventy new cities, such as Alexandria, Egypt. At its peak, Alexander's empire stretched from Greece to Egypt, and it even extended as far as India.
As Alexander expanded his empire, Greek culture was introduced and mixed with the cultures of the people he conquered. This can be attributed to the fact that Alexander maintained respect for the cultures of those he conquered and the fact that he allowed conquered people to maintain their culture. The blending of Greek culture with other cultures within Alexander's empire led to advances in learning, science, and education, among other things.
I believe that the successes of Alexander the Great justify his reputation. He not only demonstrated his military intelligence and leadership on the battlefield through his many victories over powerful opponents, he also demonstrated his ability to manage the empire afterwards. Alexander understood the benefits of allowing conquered peoples to maintain their cultural values even as he introduced them to the values and ideas of the Greeks. It is interesting to consider what more Alexander the Great might have accomplished had he not died at such an early age.