I have debated this quite a bit and here is my opinion on the subject

I feel that when an era begins and an old one dies, there needs to be some form of REAL DRASTIC change in the world....for me I believe that one of the most drastic changes to the world in ancient times was the rise of Islam. The rise of Christianity was slow, gradual, and although much changed, the empire continued on, it just switched gears.
The rise of islam was a drastic change in world power structure. From around 600 A.D. Muhammad and his followers and kinsmen spread and empires fell and Islamic empires rose in their place and almost anyone who apposed them paid the price.
This is not a statement on the nature of islam but on the quick rise and spred of this religion and how it changed the power structures and changed world dynamics. I think the rise of islam solidified a division between east and west and the true death of the pagan world and a solidification of the monotheistic era.
The rise of islam was like an army on the march, not just Muhammad but his descendants and the right caliphs that would end up starting the great islamic empires, a large portion of the areas taken in the initial spread...Arabs lands, north africa, middle east, and eventually the near east remain islamic today and in some ways the lines are still drawn as they were in the beginning, both sides, with us or against us.
The rise of islam truly injected a brand new factor and no insignificant one as from almost the beginning islam spread, not like Christianity, underground, but as a fierce movement that spread by any means. It truly changed the world and we still see these changes today as the division between islamic east and western lands still survive and are still being contested.
So I voted 800 as by 700 AD islam had spread, it had by then just toppled the sassanian persians and was well on its way to threatening the west and the west was well on its way to recognizing this threat and by 1000 the western and eastern christians would begin putting aside their differences in the face of this threat.
580-620 AD
this is a coin of Khushro II, the sassanian king who was contacted by emissaries of muhammad...this is said to be what transpired at that meeting and the ramifications that I am sure he did not forsee:
Khusro II ruled during the meteoric rise of early Islam and is remembered as one of the powerful kings of the Persian Empire to whom Mohammed sent messengers with the word of Islam. He is said to have torn up the message and insulted the messenger. Ironically it would be these forces that would soon destroy the Persian Empire as a united Islamic army rapidly spread from the Arab Peninsula to engulf much of the east.
Khusro II was Succeeded by his son Kavadh II who would only reign for a few months followed by a quick succession of Kings that would end just 23 years later as Persia is defeated and over run by Islamic Invaders.
http://www.tribalsoup.com/cache/persian01.htm^^ my page for this coin
So my vote is 600-700 AD as the end of the ancient world and the beginning of the new era.