I thought America was extremely religious? At least that's the way it looks from a foreign standpoint.

In the modern way of the word, yes. I couldn't find any other states who declared themselves secular (or laïque, which is the word used in the best-known other example, France).

While the secularism is an important point in the US Constitution, there are some points up for debate. The Founding Fathers never made it a secret they were religious, think of the famous phrase of the Declaration of Independence: 'We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the Pursuit of Happiness'.

Still, it is rare for someone in a public office not to adhere to a church. Some states even have/had religious qualifications for public office, the Supreme Court ruled these state constitutional articles to be void.

Some symbolic points up for debate: the official motto of the US is 'In God We Trust', which doesn't give the impression of a secular country and the President is used to end every address with 'God bless you and God bless the US'.

In other countries, like France, the separation is much stricter. This BBC News article from 2004 is worth reading: http://news.bbc.co.uk/2/hi/europe/3325285.stm