As I would like this to be all inclusive, with me not leaving out anything that may be considered important, I would just like to get everyone's arguments for and against.
So basically, is the Jesus Myth true?
No. Which is why there are maybe 2 or 3 historians in relevant fields (NT studies, biblical studies, classical studies, jewish studies, and other historians of that era and area) out of thousands who consider the idea that Jesus never existed credible. There are lots and lots of very skeptical scholars from all sorts of backgrounds who have waded into the historical Jesus debate, and yet they all agree he existed, had followers, was executed, and his followers began a religion (either continuing his teachings or perverting them or something in between).
A number of factors are important for understanding the reason for this universal acceptance of Jesus' historicity:
1. Sociological studies of religion. We have a good idea and a lot of scholarship on how different types of religious movement (sects, cults, etc) begin. Everything we have on the Jesus sect points back to Jesus as the founder. Whether his "real" message was lost early on, the earliest followers (even a contemporary like Paul) all point to Jesus as founder.
2. Josephus was in an excellent position to know what was going on in 1st century palestine both before and during his day. He mentions Jesus twice, and even if we threw out the longer reference as entirely spurious, the other reference names Jesus' brother, who was alive while Josephus was, and who was tried publicly in a trial Josephus knew about. This alone is more evidence for historicity than for many names that come down to us from antiquity.
3. That Jesus had a brother named James is also backed by Mark/Matthew and by Paul, who actually knew Jesus' brother.
4. Careful comparisons of the gospels with the genre of graeco-roman biography have shown that the gospels fit very well as "lives" or ancient biographies. You have to remember that ancient history, whether by Thucydides or Plutarch or Diogenes Laertius, was not held to modern standards. It often contained rumor, myth, magic, etc. This doesn't make such works historically worthless, and neither are the gospels (though how well they record historical events and teachings as they were witnessed is hotly debated). At the very least however, a number of independent "lives" of Jesus, the first written while there were still people around who were alive when the story took place, shows that an early community was interested in the historical mission of their founder, and clearly placed him in a historical time and place not long before.
History is all about trying to come up with the most plausible explanation for the available evidence. There is no better way to explain the evidence than that Jesus existed, inspired a following, and soon after his death his followers were interested in immortalizing his teachings, acts, and story.
whom can be shown to be a compilation of earlier myths and legends.
Most of these "compilations" I have seen are extremely poor. For example, there are all sorts of comparisons between Jesus and Mithras, only the dying and resurrecting Mithras was the hellenistic one, and dates to about the beginning of the 2nd century CE, after at least three and probably all four gospels are written. Other comparisons take tidbits from this or that myth out of context and then attempt a comparison. Then there are the lists of comparisons like the one logician posted sometime ago that are chock full of outright historical errors and references to parts of myths that simply aren't there.