A correct interpretation of Luke 2:2 requires taking into account a key item of historical information of a most practical nature: any census of subjects (as opposed to citizens) of the Roman Empire was carried out for tax purposes, to determine the taxable base of each subject. In such a census, people to be registered were not expected to travel but to do exactly the opposite: stay in their homes and wait for the census officer, who was above all a tax assessor. Josephus, in his description of precisely the census ordered by Quirinius in 6 AD, explicitely states that the registered people had their possessions assessed, including land and livestock (AJ 18.1-3, quoted in the Jul 20, 15 answer by Dick Harfield). And it is evident that Joseph did not have properties in Bethlehem, otherwise he and Mary would not have had to seek shelter in a manger for Mary to give birth.
Therefore, the historically informed translation of Luke 2:2: "hautē apographē prōtē egeneto hēgemoneuontos tēs Syrias Kyrēniou" is "this registration took place before Quirinius was governing Syria". Note that rendering "prōtē" as "before" is consistent with the established translation of the end of Jn 1:15: "hoti prōtos mou ēn" = "because He was before me".
Thus, noting from Acts 5:37 that Luke was fully aware of the event of Quirinius' census, its nature and its consequence, namely the uprising of Judas the Galilean, the reason of his mentioning the event in Luke 2:2 becomes crystal clear: state for the record that he was not talking about that census. I.e., Luke is saying: "Given that in a Roman census of imperial subjects people remain at their homes, I state for the record that the census that prompted Joseph and Mary to travel to Bethlehem was before Quirinius ordered his infamous one."
How then could it come to pass that Luke's statement was interpreted for centuries in exactly the opposite way as he meant it? Because of complete unawareness of historical context. I imagine that anyone living in the Roman Empire at that time would find this discussion hilarious to the point of ridiculous, and think: "How can these guys not understand that a census of subjects of the Empire (as opposed to Roman citizens) is for tax purposes, and that people must wait for the census officer at their homes? How else could the census officer reckon the taxable base of each person other than having a look at his property?"
On the other hand, the census that prompted the travel of Joseph and Mary was ordered by Herod and obviously restricted to the territory ruled by him. It approximately coincided in time with a global census ordered by Augustus in 8 bC, but was of different nature. Whereas Augustus' 8 bC global census was restricted to Roman citizens and for statistics, not tax, purposes , the motive of the Census ordered by Herod in 7/6 bC was that all his subjects should swear fidelity to Caesar and King (AJ 17.42) . Together with the record of the oath, people were registered for an egalitarian contribution per capita in the way ordered by Ex 30:11-16, in which the possessions of each person were not taken into account.
In the context of a registration ordered by Herod, and knowing his profile, the order that all descendants of King David should register in one place was wholly plausible and logical, as it allowed Herod to know all potential claimers to the throne of Israel (and hence potential threats to his position). Furthermore, it is highly likely that the duty to travel to the city of their ancestors was in force only to King David's descendants, because of the people in general Luke says that "all went to be registered, each to his own town" (Lk 2:3), not "each to the town of his ancestors".
 Res Gestae Divi Avgvsti Chapter 22 (The Deeds of Divine Augustus) translated by Thomas Bushnell, BSG. Available online at: http://classics.mit.edu/Augustus/deeds.html#71
 Armand Puig i Tàrrech, "Jesus: An Uncommon Journey : Studies on the Historical Jesus", Mohr Siebeck, 2010. Chapter 2 "The Birth of Jesus", Section 4 "A More Judaico Census Decreed by Herod", pp 74-84. Partially available online at: