This question is addressed here: http://www.comereason.org/roman-census.asp
The article cites references that corroborate that Rome periodically conducted censuses, and that Caesar Augustus made frequent use of the practice. Some were widespread, while other were restricted to a single region. A brief quote:
Indeed, it seems that Caesar Augustus was the type of leader who
ordered many censuses in his day. Records exist to show that
Roman-controlled Egypt had begun a census as early as 10 B.C. and it
was repeated every 14 years. And Augustus himself notes in his Res
Gestae (The Deeds of Augustus) that he ordered three wide-spread
censuses of Roman citizens, one in 28B.C., one in 8 B.C. and one in 14
A.D.2 In between there are several other censuses that happened
locally across Rome. Luke's account corroborates the idea of multiple
censuses for Judea when he writes "This was the first census taken
while Quirinius was governor of Syria." Certainly, the word "first"
implies that more than one census happened.
The article also suggests that Quirinius may have served in Judea on two occasions, once as procurator in charge of the census, and later as governor, in light of the different terms used to describe the two roles.