Since Christianity has had such a huge impact on the Western world for thousands of years, this is difficult to say. If it's true what's been said so far, that without its influences both Judaism and Islam wouldn't have spread or gotten developed, then something else would have taken the place. An evolution of Roman gods? A conversion of them to a more monotheist one? Some type of enlightenment that prevented any large religion from growing at all?
Even if Christianity had never caught on, I think that late antique culture would have still moved in an other-worldly direction. That was the general intellectual current in those centuries and we see similar things happening among the pagans too. So whatever sort of religion(s) might have existed in late antiquity in the absence of Christianity, it would have probably had its eyes focused on a supposedly higher transcendental realm and would offer people some sort of salvation. All in all, my guess is that what we would likely have today would be something resembling Indian Hinduism, except without the castes and perhaps with less emphasis on karma and rebirth. In other words, we would have a syncretistic mix of all kinds of deities and religious currents that were current in the ancient Roman world, along with new ones imported from the Germanic pagans and wherever else in centuries since. And arching over all of it, giving the whole thing some philosophical coherence (much like Vedanta's role in Hinduism) would probably be some offspring of Neoplatonism. This religious philosophy would interpret the many gods inherited from ancient polytheism as diverse manifestations of a single ineffable One. After all, the religious situation in India wasn't tremendously different than the situation in the Greco-Roman west in ancient times. What we see in India today is the continuation of that ancient inclusive tradition down to the present, while in the West it was swept aside and replaced by far more aggressive and intolerant Semitic traditions imported from the Middle East.
