The results from a recent Harris Interactive Poll, taken in November of 2013 and published a month later, show a continual decline in Americans’ belief in the supernatural, which I take to be part of the inevitable secularization of this country. The sample size was 2250 adults over age 18, the poll gives no error limits on its estimates as it’s impossible to gauge error on issues like the beliefs of who didn’t respond, the wording of questions, and so on.
The good news, as I said, is that belief in things numinous and supernatural is on the wane; the bad news is that belief in religious superstition still far exceeds the acceptance of evolution.
Here’s the critical data: belief in evolution and the supernatural and paranormal between 2005 and the end of 2013. As usual, belief in things like miracles and the afterlife, as well as angels, hovers around 70%, but, as you’ll see in the last column, the percentage accepting such phenomena has dropped appreciably since 2005, with belief in God alone declining 8% in the last 8 years. If that trend continues, America should be completely atheistic by 2088! That won’t happen, of course, but note that most of the drop happened within the last four years. (Because of that, one has to wonder if the new figures are somehow anomalous).

Acceptance of evolution has risen 5%, while that of creationism has declined by 3%; and acceptance of most paranormal phenomena, while showing a slight increase, is still appreciably below that of religious “supernatural” phenomena. Still, it’s a bit discomfiting that 42% of Americans still believe in ghosts!
Take a look at this table about degree of certainty that there is or is not a god; figures involve four polls over ten years.

Absolute certainty of God has gone down 11%, and if you cound the last three rows as “atheists/agnostics,” that figure has risen from 21% to 32%—a remarkable 52% increase in 10 years.
That secularism mirrors the change in people’s self-description, in which the “not at all religious” category has increased from 12% to 23% since 2007:

As expected, the South is more religious than other areas of the country, and Republicans are more religious than Democrats:

Add to this table a partition by age (below), and you’ll see a steady increase in religiosity with age of respondent. This suggests a “cohort effect”: older people were more often brought up religious and have retained those beliefs. But there’s an alternative explanation: older people become more religious as they get older. I don’t have the data at hand, but I think that evidence from other polls, as well as from this one—the cross-section of Americans shows a general decline in religiosity, although the mean age is likely to be similar among all polls—suggests that some of this is a general decrease in religiosity in more recent years.
Remember, these data are percentages of people certain that there is a God:

In contrast, scientists working at “elite” universities show the opposite trend (this is from other data I’ve discussed): older scientists become less religious. That cannot reflect either a cohort effect or more belief with age, but, I suspect, reflects a steady erosion of belief the longer one works in science.
As always, religiosity declines with education, probably for the same reasons that scientists lose faith when they get older: with more education comes more ability or exposure to critical thinking. An alternative explanation, which I find less credible, is that people who are more religious at the outset tend to leave school earlier:

There are other interesting data in the poll, including what Americans think about God’s gender, but I’ll let you look for yourselves.
One figure did surprise me, though: the percentage of people who think God concerns himself (herself or hirself or zeself or whatever) with what happens on Earth:

I’m trying to comport this with my observation (personal, of course) that most religious Americans are theistic, believing in an interactive God. The figures above, however, suggest that more Americans are deists (“does not control what happens on Earth”) rather than theists, though the most striking figure is in the last row—nonbelievers.
At any rate, perhaps theism is more than simply God’s “control” of what happens on earth, but can also involve God’s “interaction” with Earth’s inhabitants. That is, theists might not believe that God changes things, but still has a meaningful dialogue with and a personal interest in believers. Still, the 29% of all adults who believe in a non-active God is a puzzle to me. Perhaps the question could have been worded better.
If one can trust these results, they document the increasing secularization of America—a secularization more rapid than I would have expected. Perhaps one happy day we’ll be like Denmark!