Many of the so-called "Jesus Mythicists" deny that there was any historical Jesus whatsoever. Specifically, though, I want to focus on one of their claims - namely, that the narrative of Jesus' resurrection was something that Christians borrowed from pagan sources. The name of Osiris is usually mentioned during these exchanges. Let us, for the sake of argument, assume that there really are striking parallels between Jesus and Osiris. Does the Jesus Mythicist now have a case? I believe he does not.
For one thing, there are also parallels to be found between the pseudo-mythical King Arthur and the historical King Henry V. Both men were brilliant war commanders of Great Britain who had enormous difficulties with their subjects. Does this mean that what we know of Henry V is now bunk? Surely not, and that should give us an incentive to reject the original Jesus Mythicist claim that the early Christians borrowed from their pagan neighbors. This becomes even more vivid once we consider how vague some of the alleged parallels really are.  That both were resurrected (in some sense; the Jewish conception of resurrection was bodily in nature) does not at all imply any borrowing.
In addition to this, we may consider the fact that there are many historical facts in support of Jesus and Henry V (see the book below). We're still waiting to hear about actual evidence of Osiris and Arthur.
 Gary R. Habermas and Michael R. Licona, The Case for the Resurrection of Jesus, Kregel Publications, 2004, p. 91