The U.S. Census, which is coming up this year, does not measure people's religion, but it turns out that wasn't always the case. In the 1800s, it included some interviews of clergy about their flocks, and this provides a statistical portrait of U.S. religion at that time, and this type of information was collected through the middle of last century. (Rodney Stark and Roger Finke have made good use of these data in various publications.)
I have periodically wondered about the history of religion and the census, and so I was interested to find this summary in a Pew Foundation report.
A bright side of not having Census data about religion is that Pew and the American Religious Identification Survey have stepped in and collected regular, large-scale surveys about American's religious affiliation and beliefs, and they collect richer data (albeit from a sample) than the Census would have.