I find this question fascinating: Why is it that the majority of the world's population is monotheistic? Is there some reason that monotheism is more attractive than polytheism? Or perhaps monotheism allows for a more successful empire? Or is it simply a coincidence of history? Or is it better rephrased as: Why are the two largest religions derived from Judaism?
Three thousand years ago, the vast majority of the world was likely polytheistic. Then Judaism developed, but was not widespread. Around 600's BC Zorastrianism (monotheistic) developed, and became one of the world's largest religions thanks to the spread of the Persian empire, but declined in 300's BC after Alexander the Great toppled the empire. So again by 0 AD there were very few monotheists. Today there are approximately two billion Christians and 1.5 billion Muslims, with a current world population of 6.7 billion (see here for breakdown). By contrast there are 1 billion Hindus (polytheistic). There are around 1 billion Buddhists (Buddhism, in it's original form, is neither mono- nor polytheistic as the Buddha simply taught how to reach enlightenment but did not identify particular gods, however many later forms developed local deities and divine figures). In other words, monotheism likely developed relatively late in human history, yet now most people are monotheistic.
1) My initial thought is that monotheism has become more popular due to it being more reasonable to the rational mind than polytheism: For the modern person, science has come to explain most of the concepts that previously required supernatural explanation. A science-minded person tends to believe either in no god, or in an unknowable god that was responsible for the creation of the universe. For Christians, Muslims, and modern Jews, God is similarly unknowable: God is judge, lawmaker, and can control events, but does not have a personality or form. (Granted, in parts of the Old Testament God has a personality, as when he walks in human form around the Garden of Eden, or argues with Satan about how faithful Job is, but these stories feel out of place compared to the usual sense of the formless and abstract God). Alternatively, in a polytheistic religion such as Hinduism or Roman paganism, gods are frequently less abstract and have particular personalities. For instance Vishnu is often pictured with four arms, riding on his eagle Garuda. (That said, Hinduism has a diverse range of thought and, unlike Roman paganism, has versions that are monotheistic.) In summary, it seems that belief in a single abstract god is less at odds with a scientific worldview than a group of personal gods with character and form. Thus it's not surprising that as the world has become more aware of the scientific viewpoint, we find that monotheism has become more popular.
2) While I really like the above idea, it is not really borne out if you look at the historical details. In reality, many people are Christian or Muslim as a result of historical empires and colonization.
Background: The Roman empire was pagan for most of it's history but converted to Christianity in the time of Constantine in 300's AD. Thus Europe became Christian. Then Europeans, through colonization and proselytization, led to Christianity in the Americas, large parts of Africa, Australia, and many smaller areas. Also, after the fall of the Roman empire in 400's AD, the eastern "Byzantine" half of the Roman empire lived on and was responsible for spreading Christianity to Russia. I am less familiar with how Islam spread, but generally it spread initially through the conquests of the Arab Empire in 600's AD (Middle East, North Africa, Spain), and subsequently through proselytization along Arab trading routes in South Asia, Southeast Asia, and in parts of Africa.
So our original question, why did monotheism become so popular, can partly be boiled down to Why was the Arab Empire so successful? (I don't know enough about Arab history to answer this), and Why did the Roman Empire convert to Christianity?
3) Why did the Roman Empire convert to Christianity? You might think it was political. Yes, Constantine converted to Christianity, enforced religious tolerance, and halted persecution of Christians throughout the vast Roman Empire. But leading up to this point, Christianity was spreading rapidly in spite of political opposition and persecution. So while later spread of Christianity can be explained primarily by political events, at least the early spread of Christianity was a result of organic growth. And why was Christianity spreading so quickly, at first mostly among the lower classes of the Roman Empire? This is a question with, I would guess, lots of contributing explanations. But I think it boils down to a) One of the tenets of Christianity is the importance of proselytizing, and b) Christian teachings were particularly attractive to the lower classes (i.e. the meek shall inherit the earth, a rich man is unlikely to go to heaven, Jesus is the son of a humble shepherd and focuses his teachings on lower classes, an eternity of happiness awaits you at death, etc.).
So how does this relate to the original question: why did monotheism become so popular? Is it a coincidence that Judaism, at first the only monotheistic religion of the Roman Empire, and a small minority religion, produced an offshoot that spread rapidly through the Roman Empire? And then produced another offshoot that led to Islam and the Arab Empire?
Jesus' teachings are thought by modern scholars to be heavily influenced by the Pharisee sect of Judaism that was growing in popularity during his lifetime. Some Pharisee writing, preceding Jesus' life, sound similar to New Testament teachings: "That which is hateful to you, do not do to your friend. That is the whole Torah." -Hillel the Elder, 1st century AD. "A learned bastard takes precedence over an ignorant High Priest." And the Pharisees, unlike their theological opponents the Sadducees, believed in resurrection of the dead. The Pharisees are considered more democratic than the aristocratic Sadducees. At the time of Jesus, the Pharisees were a minority sect among the Jews, but their philosophy turned out to be quite popular and shortly after Jesus' death would become the majority view of Judaism, and is the forebear of Rabbinic Judaism. Thus Jesus' teachings were not coming out of the blue; they were a development of contemporary Jewish ideas that were themselves evolving through theological debate within the Jewish community.
Thus again we can boil down our original question partly by asking: Why did Judaism, via the Pharisees, produce this very attractive and self-multiplying version of itself where other contemporary religions did not?
To help answer this question, let's start by asking: How was Judaism different from other Roman religions? As the Roman Empire spread, the cults and gods they encountered were often incorporated into the Roman pantheon. People were free to continue participating in local cults as long as they agreed to participate in the traditional Roman ceremonies as well. Jews, initially the only monotheists in the empire, refused to worship other gods. At times this caused problems, but at other times they received special exemptions from the state. Thus Judaism was unique in that, through the fixed monotheistic dogma found in the Torah, it was not able to be assimilated like other religions. In fact we see that today, with Judaism being one of the oldest surviving religions in the world, despite numerous periods of persecution and exile. Thus it appears that monotheism helps a religion resist assimilation.
Is there a relationship between monotheism and proselytizing? Hinduism and Buddhism usually avoid proselytizing and believe there is more than one true way (Hare Krishna's are an exception). Judaism does as well. However, both Christianity and Islam believe there to be only one true way and place great emphasis on winning converts. It seems like an easy step to go from the self-confidence and immutability that is inherent in monotheism, to believing that other religions are incorrect, and thus believing in the necessity of proselytizing. Is this true? If monotheism tends towards proselytizing, then this would seem to be the key answer to the original question. Historically, most religions are polytheistic and most religions do not proselytize. However, the two largest religions worldwide run counter to this trend: both are monotheistic and proselytize.
In conclusion, I think the reason for the ultimate success of monotheism is likely related to its inability to be assimilated into other religions, its tendency to believe that other religions are incorrect, and its tendency to lead to proselytizing. (This is similar to evolutionary biology: genes spread that assist individuals in a) surviving to adulthood, and b) procreating. Dawkins would call monotheism a successful "meme.") In addition, it was incidentally helpful that the Roman Empire conquered Jewish territory, allowing an attractive and accessible offshoot of Judaism to spread throughout the empire, an empire that would be a major foundation for European and ultimately global culture.
I'm very interested to hear your thoughts. Please leave a comment.
Note that a previous version of this post incorrectly asserted that Pharisees proselytized. My evidence for this was very weak. Thanks to Esther for pointing this out.