What made Alexander great?

1. The Charisma - Macedonian soldiers were ready to go with Alexander, because they loved their leader and didn't just go with him because of fear of him.

2. The War techniques - Alexander was "great" at designing new techniques at war. For example, He let the war chariots go inside his line and made his warriors attack the chariots from behind. The chariots then weren't able to attack the soldiers behind them. Literally, this technique made the war chariots become useless for backward attack.

3. The desire - As per my studies he had grown up with the dream of "EAST".:)

4. He did everything as if he was predestined to. So that he has become "Great".

The Greeks had demonstrated military superiority over the Persians for many years. Both Cimon and Agesilaus had led successful expeditions into Persian territory. That Persia maintained its dominant position over Greece had not so much to do with their own military capabilities, but rather because of the incessant warfare amongst Greek cities. Their focus on destroying each other drained their resources and enabled Persia to make territorial gains in exchange for money supporting one side or another in the Greek wars. Plutarch lamented that when Agesilaus met with success in Asia Minor and was intending to march on to the Persian capitals, he was instead ordered back to Sparta by the ephors to fight against other Greeks.

The Macedonia that Alexander left behind was very different to the Greek city states. Alexander did not have the restraints imposed by ephors, voters and term limits, so had much freedom in his military planning. Macedonian conquests under Philip and during Alexander's early reign set the foundations for the conquest of Persia. The subjection of their neighbours, including a weakened Greece, enabled Alexander to march without fear of suffering Agesilaus' plight. The conquered wealth, including from the gold mines of Amphipolis, could pay for a military substantially larger than that under Agesilaus while still leaving enough troops to protect the homeland. The allure of Persian treasure was also a great incentive for those in the much poorer Greece to take to arms.

I do not share Livy's assessment that Alexander would have failed against Rome. The situation of Perseus is not a valid comparison. At that time, Rome was already the dominant power of the western world while Macedonia had lost much of its power and was commanded by less capable generals. A better choice would be the example of Pyrrhus, commanding a smaller territory and fighting some 50 years later when the Romans had grown in power, who was successful in battle against the Romans but ultimately lost the war due to insufficient reserves. Alexander was better resourced and would not have had this problem. More importantly, the Romans had not in Alexander's time adopted the tactical changes that would give them superiority over phalanxes in later years, so he would also not suffer as severe losses as Pyrrhus did.

Alexander would not have been able to defeat Carthage, as that would have either required naval superiority or a massive overland march.

I voted up lins314159's answer. I would like to add a couple of things though.

The vast majority of Alexander's empire actually started his tenure as the Persian's empire. So a great deal of credit (and attention) should be paid to all the work they did to put that empire together.

However, Persia's loss of the Persian-Greek wars 100 years earlier had established that Greek arms were superior. After that, what kept the Greeks in check was mostly Greek infighting (which Persia happily subsidized). At this point, Persia's biggest nightmare would be the Greeks uniting and turning against them.

Enter Phillip of Macedon (Alexander's dad). Probably the one thing he had that nobody else in Greece had was rich silver mines in his territory. In fact, the first place he took was Amphipolis, which contained the silver mines (and some gold too). Wikipedia talks a lot about Phillips expert diplomacy and his military buildup, but both were financed with Macedonian silver. Using those resources, he slowly conquered or acquired the submission of all of Greece, save Sparta (and Crete, if it counts).

Then he was promply assasinated, leaving his heir Alexander with a huge and expensive army to feed, and the hapless Persians right next door...