Because everyone seems to enjoy inferring arguments in my posts that I'm not making, I'll make it explicit from the outset on this one: This is to point out a single contradiction between two of the gospels. I am not attempting to discredit every word of the Bible, disprove religion, insult your mother, etc. Mainstream Christians probably won't even be phased by this. However, if you take the Bible to be the infallible Word of God, then this is meant to give you pause for a second. Aside from that, I just wanted to bring up a few points about how the gospels address this topic that might be of some interest.
One of the easiest contradictions to find within the Bible is that of the two genealogies of Jesus, the first in Matthew 1, the other in Luke 3 (neither Mark nor John include a genealogy). In viewing the two (placed in convenient column format to your left), a few things should be apparent. Both start with David, and end with Joseph and Jesus (in fact, both trace David back to Abraham, Luke even going further back all the way to Adam, but since these parts of the account agree, they are irrelevant to the topic at hand). Aside from David and Jesus, only four names are shared between the two lists.
Matthew has 28 generations, and Luke has 43 between David and Jesus. This can be accounted for by tracing Jesus' lines through two different descendants
of David, Matthew through Solomon and Luke through Nathan. Presumably the lines cross again at Salathiel and Zorobabel, then diverge again until reconvening at Joseph, although it is never explicitly stated as such (maybe Salathiel and Zorobabel were common names back then).
Then we run into the obvious issue that Joseph seems to have a different father depending on which gospel you study. The common apologetic response to this is that one of these accounts traces Jesus' lineage through Mary. This would make sense at first glance, until one realizes that Mary is not mentioned anywhere in Luke, and only arises incidentally in Matthew.
The format Matthew's genealogy takes is straightforward, reading of the vein "Azor the father of Zadok, and Zadok the father of Achim, and Achim the father of Eliud," and so on until: "Matthan the father of Jacob, and Jacob the father of Joseph the husband of Mary, of whom Jesus was born." The only reason the format changes at Joseph is because Matthew makes it quite clear that Jesus was the result of a virgin birth, so Joseph was not technically
Jesus' father. To claim that this is the genealogy of Mary becomes difficult to argue, since what is the point of having a genealogy if every single person listed isn't related to the person whose ancestors are being chronicled? Both genealogies clearly pertain to Joseph, not Mary.
More evidence for this view can be found when it is noted that not a single genealogical record of any woman within the Hebrew Bible (Old Testament) or in any other part of the Greek Bible (New Testament). In fact, once place in the Bible, in Numbers 1:18, we are given an example for how at least this genealogy was assembled: "...declared their pedigrees after their families, by the house of their fathers."
One of the main reasons Jesus' genealogy was included in these gospels was to fulfil the Jewish prophecy that the Messiah would be a direct descendent of David. Apparently for the authors of these gospels, being the son of the wife of a descendent of David was close enough. This again lends credence that neither genealogy was of Mary, since women were not entitled to be heirs to the throne of David, meaning Mary could not pass on what she never herself possessed. Knowing this about why these lists were put in, we see a problem with the list in Matthew. Jeremiah 22:28-30 has YHWH proclaiming Jechoniah "as if childless... none of his offspring will prosper, none will sit on the throne of David." If none of Jechoniah's children were to be part of the Davidic legacy, how can Jesus be if he is descended from Jechoniah's child as Matthew 1:12 states? Jesus would be under the curse of Jechoniah.
The final problem we find with the concept of these lineages is that of direct descent. According to Jewish prophecy, the Messiah would be a blood descendent of King David (2 Samuel 7:12-13, Psalms 89:3-4, 132:11). Obviously Joseph isn't portrayed as a flesh and blood relation to Jesus, so Jesus cannot be a flesh and blood relation to David through Joseph. Even if one does take Luke to be the ancestry of Mary, 1 Chronicles 22:9-10 tells us that the Messiah will also be descended from Solomon, but we see that the line Luke traces goes through Solomon's brother, Nathan.