Anyway, my class has been learning about Western Civilization, and Alexander the Great pops up. He was an amazing general and leader of Macedonia, and conquered most of the known world back then. He encouraged the mixing of cultures, and therefore that led to the Hellenistic age, where many new ideas popped out that still influence us today. He destroyed the Greek city-states, which led to an opening for Rome to come in and start their tremendous influence and power on Western Civilization. He built many cities, many of them named after him; the most famous being Alexandria, Egypt. 

However, he was theorized to have been an alcoholic for the majority of his adult life, and led to a murder of one of his friends, Cleitus. Also, the burning of Darius the Great's palace in Persepolis was probably due to a drunken rage. Alexander would normally never destroy monuments in violence. He also set up an empire that could not last without him, and therefore the empire totally crumbled when he died. 

There are probably much more pros and cons for A the Great, but do you think he deserved the title "the Great"? 

The empire may well have endured if he had actually taken steps in life to prepare a successor.
At any rate he does deserve the title.
He was the eastern napoleon, the western genghis khan. He knew what he wanted and he knew how to get it.
A master of strategy and a truelly unbelievable undertaking. No foundations were laid for him, he built his empire from next to nothing, managed to remain the strongedt empire in a state of near constant war, and with a few later exceptions, i think expanded his empire further than any other under 1 rulers lifespan.
Its not even that he ran out of time, he died young and things could have been vastly different if he had survived a few more years.

You know greece refuse to recognise the modern nation of macedonia because their is a region in greece called macedonia, and they feel that it undermines their territorial integrity.
Random titbit.

Alexander was well known to be a paranoid, violent, and cruel drunkard. His title had everything to do with his status and military success, not his upstanding moral character.

He might be. But there were much better commanders than him throughout history. Napoleon conquered Europe, twice! And Genghis Kahn conquered an area 5 times the size of the "known world" referred to by most historians. He was impressive for doing what may be the closest anyone will get to world domination though. Seeing as how he took over all of the notable (useful, rich, ect.) spots in the world. He overlooked his empire security, as it crumbled.