In recent years - thanks in large part to the Internet - there has been a lot of talk and discussion about the influence of pagan ideas and beliefs on the rise of Christianity. A few years back, there was an Internet movie called Zeitgeist that caused quite a sensation in this regard. It was ultimately a film about how 9/11 was an inside job, but the first segment of the film discussed some incredibly provocative theories about the origins of Christianity and its connection to pagan beliefs - particularly the religion of ancient Egypt.
I wrote a long and scathing critique of the movie's religion segment a few years back, so I won't repeat myself here, other than to say that virtually the entire thing, from beginning to end, was balderdash of the most insidious kind. Be that as it may, the movie has helped to spark some healthy debate on the subject. There have also been some books out recently discussing these topics, though I have not personally read them.
To put it simply, I think the question of pagan influence on Christianity turns first on what aspect of Christianity one is talking about. In terms of Christian theology and doctrine, there can be no doubt that paganism had a profound effect. Beginning in the 2nd century, Christianity had become almost exclusively "Gentile" - that is, non-Jewish. A a full-blooded Jewish sect in the 1st century, Christianity went through a painful separation in the last few decades of that century and by the year 100 or so, it had essentially become a whole new religion.
As a Gentile religion, it sought converts from among the pagan religions of the Roman empire. Like any religion, most of its adherents eventually came from within - that is, they were born to Christian parents. But in the first few centuries of Christian history, many, many former pagans converted to the new religion, particularly in the 300's C.E., after it became the official religion of the empire. It was during this same time, of course, that much of the theology and many of the doctrines Christians still follow today were developed and put into practice. As such, pagan beliefs that converts brought with them deeply and greatly influenced the development of Christian theology and doctrine.
Consider, for instance, the doctrine of the Trinity, which could easily be viewed (particularly by an outsider) as watered-down polytheism: three gods in one, separate but equal. This doctrine was formulated during those early centuries when pagan (i.e. polytheistic) beliefs were still common.
Related to that issue is the question of the divinity of Jesus. This was a huge issue in the early church, particularly during the 2nd century. Was Jesus God or man? Divine or human? The Trinity, of course, ultimately answered that question for Christians, but the very nature of the debate was the result of non-Jews attempting to understand the distinctly Jewish stories about Jesus. I am firmly convinced that no self-respecting Jew - even a Jewish Christian - would ever have considered Jesus to be one and the same with God. Such a notion would have been so fundamentally contrary to all that it means to be Jewish that only non-Jews could have considered it. Jesus-as-God is a notion that did not arise in Christianity until it became a Gentile religion. Among pagan religions, the belief that humans could be gods was commonplace, so common, in fact, that it's one of the defining characteristics of many ancient religions. It is not surprising, then, that the Gentile-dominated early Christian church was amenable to the notion of Jesus being one and the same with God - a notion that would likely have left Jesus's earliest followers, not to mention Jesus himself, in the stunned silence of a major blasphemy.
So on that subject - pagan influences on Christian doctrine and theology - there is no doubt that it played a major role.
This, however, is not particularly controversial. What is far more provocative is the idea that paganism influenced the very telling of the Jesus story itself. Forget 2nd and 3rd century institutional doctrine; these theories suggest that Jesus may never have existed at all, and whether he existed or not, the stories about his life were developed from pre-existing themes in ancient religion and don't really represent anything historical.
These theories and arguments make for good fiction - and if you ask the producers of Zeitgeist, probably a lot of money too - but in my opinion there is very little of substance to them. Zeitgeist, as I said, is a pack of lies from beginning to end, but even among the more "mainstream" theories of pagan influences on Christianity, most of it is unfounded speculation.
One thing that any reputable historian of early Christian history will tell you is that the stories of Jesus, and the entire gospel tradition, is a deeply and profoundly Jewish one. Indeed, the inability (or unwillingness) over the ages of institutional Christianity to recognize the distinctly Jewish nature of Jesus and the stories about his life is, in my opinion, one of its biggest failures. There is virtually nothing in the gospel tradition about Jesus that cannot be traced to some aspect of Judaism and Jewish history and tradition.
Consider, for instance, the story of Jesus' birth. This is one of the more popular stories that the revisionists like to link to paganism. There's no question that Jesus wasn't the first person in history to have a virgin birth story connected to him. Therefore, Luke and Matthew must have drawn it from pagan sources, right? Not necessarily. All the themes from these accounts of Jesus' birth can actually be traced right back to the Old Testament - the Jewish scriptures. For crying out loud, Matthew even quotes Isaiah to back up his claim that Jesus was conceived by a virgin. This idea doesn't come from pagan influence - it comes right out of the sacred scripture of the Jews!
The same is true for many of the other stories about Jesus's life. Consider the 12 disciples of Jesus. I tend to think that the notion of an inner group of exactly 12 men is a creation of the primitive Christian community. I think the truth is that Jesus probably had a lot of followers, some of whom came and went. There was probably a core group that was with him the longest, but it wasn't necessarily exactly 12, and later there was a lot of controversy over who, precisely, had been part of this inner circle. If this is correct, then we need to explain where the notion of "12" came from. The pagan-influence theories suggest the 12 signs of the Zodiac (I think this is an argument made in Zeitgeist, in fact). But this, of course, is silly. Clearly the 12 Tribes of Israel would be the logical conclusion about where the notion of 12 disciples may have originated. There is even a quote attributed to Jesus making this explicit comparison, when he tells his disciples that they will sit on 12 thrones judging the 12 tribes of Israel. Furthermore, it is a perfect literary creation: just as the original 12 sons of Jacob became the patriarchs of the Jewish people, so the 12 disciples would become the patriarchs of the new Christian community, with their converts becoming the new 12 "tribes" - the new people of God.
Ultimately, whether the existence of exactly 12 disciples is history or legend, it is distinctly Jewish, not pagan.
In the end, I think it goes without saying that pagan beliefs had a lot of influence on later Church doctrine and theology. I do not, however, think that pagan traditions had much influence on the telling of the stories about Jesus. In fact, I'm not sure there is any reason to suppose that any of what we find in the gospels comes primarily from pagan tradition. Now it's true, of course, that Judaism itself, by the time of Jesus and the gospels, was greatly Hellenized. But only inasmuch as Judaism itself had been influenced by Greek culture and philosophy did any pagan thought, myth, or tradition play a role in the development of the gospels about Jesus.