To answer this question, it is important to understand that while there is a clear contrast between pure polytheism (e.g. early Greek mythology) and pure monotheism (e.g. Islam), polytheism itself has a number of gradations.
Many religions deemed polytheist believe, for example, in the existence of many gods but worship only one considered the supreme being; a practice known as inclusive monotheism or Henotheism. There is also the belief that multiple Gods are different manifestations of a single divine power; this is the bedrock belief, for example, of the Hindu Smartas, and was argued by the Modalists to be an interpretation of the Christian trinity.
It is a tenet of Western history that the religious culture evolved from polytheism to monotheism. The evidence for the antiquity of polytheism is obvious; the early Egyptians, Sumerian, and Akkadians were all polytheists. Furthermore, comparative study of the various polytheisms of Western Europe hints that they may have derived, like Indo-European languages, from a common Proto-Indo-European Religion.
The short-lived monotheistic revolution of the Egyptian pharaoh Akenaten involved the elimination of all but one god in the Egyptian pantheon. This point is important because Akenaten’s destruction of all the newly false idols finds reflection in e.g. the Ten Commandments (God’s first/second commandment does not say there are no other gods, but that no other gods will be “held before” him, implying symbols of their worship should be destroyed). In my opinion this shows a general tendency for monotheism to drive out older polytheist beliefs. As someone noted earlier on this thread, there is an inherent tolerance built into polytheism, whereas monotheism by definition cannot accept another culture’s gods.
Zoroaster represents another important step in the development of Monotheism. Despite the underlying dualism between the Spenta Mainyu and the Angra Mainyu, these are clearly a clash of concepts–something like the struggle between the concepts of good and evil–and both are subservient to the all-powerful single god Ahura Mazda. In short, the religion’s metaphysics are cast as dualism, but worship and devotion were monotheistic.
But the importance of Zoroastrianism was its adoption by the Persians just as they were beginning to build an empire across the Near East. Religion and state power were inseparable in ancient cultures, and once a monotheistic religion was adopted by a ruling class in a powerful enough nation, it seemed inevitable it would spread as far as military and political power would take it.
One poster remarked that “polytheism hasn’t fully yet evolved out of the major religions at all,” and cites as an example the role of the saints in some Christian religions. It may indeed be human nature to ascribe the assumed unseen powers hovering over different aspects of life to different supernatural forces, and the Christian role of saints as intercessors is perhaps an accomodation of this tendency. But monotheism in general relies upon an ascent of mind and will to overcome indulging this tendency. By comparison, Christian religions accept the presence of sin even though the main goal of the religion is to avoid sin. In that sense monotheism may truly represent a mental evolution, but I’d hesitate to apply that to non-Western religions.