Ever since 1972 the General Social Survey has polled adult Americans' opinions on a variety of subjects using in-person interviews. The latest results, based on a survey conducted in 2014, have recently been released, and they're quite interesting. The Associated Press has a good overview at this link, and the report itself can be found here. (That page is a brief summary with links at the right to PDF and HTML versions of the full report.)
The number of those surveyed who don't identify with a specific religion has reached a new high of 21 percent, up from just 5 percent in 1972. Moreover, only 70 percent express belief in an afterlife, and only 58 percent in God. But on the other hand, just 3 percent are explicitly atheists and another 5 percent agnostics. I suspect one reason for the seeming discrepancy is that for many people, including a fair number of those who consider themselves members of a particular religious denomination, religion just isn't a major part of their lives or something they think about very much.
On a related public policy front, for the first time the General Social Survey finds majority support for same-sex marriage, with 56 percent agreeing that same-sex couples should have the right to marry versus only 32 percent who disagree. Among those aged 18-34, support for same-sex marriage is 72 percent.
The GSS covers a lot of other topics as well, so do take a look at the links above.