First you need to look at Alexander's army. Part of Philip II's army reforms was to ensure that it would be very mobile, to do this he reduced the baggage train. There have been instances of cities surrendering upon Alexander's arrival as they were not expecting him to come so early. That said, the Persian empire was a multi-ethnic empire consisting of Egyptians, Phoenicians, Lydians, Greeks, and countless others, many of which neither wanted to be be under the Persians or fight Alexander. Furthermore, after his enormously successful battles with Darius, many Satraps in Alexander's road map surrendered. Consider this: starting with his first battle in 334 BC and ending with his last battle with Darius in 331, Alexander had already decisively defeated Darius three times, marched through Anatolia, Judea, and Egypt, and crossed with Tigris, all in three years. That left the remaining 7 to quell Darius's supporters or pretenders and move into Asia.

I found this book particularly interesting: http://www.amazon.com/Alexander-Great-Paul-Cartledge/dp/1400079195

You have to remember that the makeup of the Persian Empire was into separate governorship's called Satrap's. The response that each satrap had for the others defense was either a response to imperial command or it was not going to happen. Also Alexander had to deal with very few uprisings against his incursions by the local populace because of his clever wheeling and dealing with Persian nobles. Ironically the toughest part of his campaign and where he DID encounter heavy resistance was in modern day Afghanistan.

Also and probably the most important factor was the incredibly professional and well designed military that he inherited and further improved upon by his father Phillip, who was a tactical and logistical visionary.