Kindest Regards, all!
Ah, a subject near to my heart!
The fertile crescent is acknowledged by archeology as the birthplace of modern human civilization. It was here that many of the technologies that humans now take for granted began: walled cities (for defense), war as an art, agriculture, the wheel, pottery, textiles, writing, mathematics, astronomy/astrology, and codified law. Even formalized religion seems to have gotten a huge boost from developments in this region. All this, before even taking Biblical accounts into consideration!
The impact of this place at that era is huge, we would all likely still be living in caves if it were not for these developments. So it is no wonder to me this place holds such significance for us spiritually, mentally and physically.
As for prophetic significance, a lot remains to be seen. I did have a professor about a year ago who was convinced that the oil fields in the south around Basra would be set alight during the war at the end of this era (ushering in the millenial age). He backed his postion with quotes from the Old Testament prophets which I neglected to commit to memory. Of course, he was a little, (how to say it politely...

) ummm, different from the rest of my profs. So I don't exactly hold his view as Gospel. But interesting just the same.
I might add, when considering Babylon, there are two significant periods historically. The era of the birth of civilization took place in Sumeria. The Classical Babylon of Nebuchadnezzor and Daniel was a different era, a couple of thousand years later, but the same geographic area.
Hope this helps for a brief foundation to build on.