This is the time of year when critics of the census account in Luke 2 are most vocal. We've discussed the issue many times at this blog. See, for example, here. In that post and elsewhere, I've recommended some resources from scholars, like Darrell Bock and Stanley Porter. There's a lot of good material at other web sites as well. For example, run a search under the term "census" at the CADRE Comments blog. Also try it with the Hypotyposeis blog.
For example, Stephen Carlson (at the Hypotyposeis blog) argues for translating Luke 2:2 as "this became a very important registration when Quirinius was governing Syria". I don't know enough about Greek to render much of a judgment of Carlson's suggested translation. But if it's correct, it would overturn some of the objections that have been raised against Luke's account.
One of the good points made by Chris Price (under the screen name Layman) at the CADRE Comments blog is that Luke doesn't say that the census required people to go to the city of their ancestry. Rather, Luke 2:4 is commenting on Joseph in particular, not all census participants in general. A more general comment is made in verse 3, and that verse only says that each participant went to "his own city", without any mention of ancestry. Most likely, Joseph had a reason for going to an ancestral city (he owned property in Bethlehem, he wanted to be associated with that city more than Nazareth, etc.), even though the census didn't require going to the city of your ancestry. Some critics not only fault Luke for allegedly claiming that the census required you to return to the place of your ancestry, but even suggest that Luke was saying that you had to go to the place of your ancestry from something like a thousand years earlier. Thus, Joseph had to go to where David lived. But the passage doesn't seem to be referring to any ancestry requirement at all, much less one that was tied to a generation a thousand years removed. The problem is with an unreasonable interpretation that's being read into Luke rather than what Luke actually said.