"Was Jesus Born in a Barn?"
UPDATE (12/22/10): Question from Charley: How is the apparent contradiction between Matthew 2 “days of " (who died 4-6 BC) and Luke 2 “when Quirinius was Governor of Syria" (AD 10-12) resolved regarding the birth of Christ Jesus and the census taken in Matthew?
This is a great question. At this point in time, we don't have direct extrabiblical evidence for the census Luke refers to in chapter 2. Scholars share wide agreement that the census in 10–12 AD is not the same one mentioned by Luke, largely for the very reason you are citing: it can't be reconciled with the death of Herod which is pretty well established. Most scholars of a more liberal bent see Matthew's account as correct and Luke's as incorrect. I'm not sure why that is, but that seems to be universally the case. For those who hold to biblical inerrancy, there are few possibilities to try and reconcile these accounts.
1. A few scholars have suggested that the English represents a mistranslation and that it could be rendered "before Quirinius was governor of Syria." This option isn't real popular, however.
2. Luke is referring to an earlier census that took place before Herod's death.
3. The KJV's translation of the term "governor" makes it sound like Quirinius had a formal title, which he did have by the time of the second census. But in the case of Luke 2:2, the term might more accurately be rendered "while Quirinius was governing Syria" or "...ruling Syria." Luke uses this same term to refer to Pilate, who technically wasn't the "governor"; he was the "procurator." And it is known that Quirinius began overseeing this area in 4 BC.
What we can say with certainty is that Luke seems to be meticulous about these kinds of details. He goes overboard to correlate the timeline of Jesus' life with prominent people. Also, there have been some incidents where skeptics have said Luke was wrong about titles, places or people, only to have an inscription uncovered which correlates with his account.