Some posit that the Founders were all Deists or atheists, others posit that the Founders were mostly religious zealots that wanted to create some kind of theocracy (with certain naughty exceptions like Franklin and Jefferson.) The truth is actually, as usual, somewhere in the middle.
The Founders were mostly externally religious. This was a time when many States had "official churches" and not to be a member of some religious body was very suspicious. Only the gentried class, such as Jefferson or Washington, could refrain from religious practice, and even then most non-religious Founders still maintained a religious externalism. For example, Washington went to an Anglican church with his wife Martha for all the years he was President, although it was noted he always left before Communion.
Most of the Founders most likely were similar to typical Protestants in mainline churches (such as Lutheran, Methodist, Episcopalian, and Presbyterian) today -- they had an inner belief, went to church on at least a semi-regular basis, and their faith informed their lives but not to the point of excess. Some were truly Deists, such as Jefferson, Franklin, Washington and Madison. Others were members of heterodox theologies, such as John Adams who was Unitarian. But what they mostly wanted to avoid was religious intolerance and religion trickling into the sphere of government.
The USA of the 18th Century was a mish-mash of religious groups, many of which were opposed to each other on both theological and legal grounds. Virginia for example was nearly an Anglican theocracy -- Jefferson helped to break that apart and create religious liberty in his home state. Puritanism reigned in the North while the South was becoming Baptist. Other sects and groups gained more or less favor, and Maryland was the only State which was highly accepting of Catholics.
The Founders saw the dangers in a State church -- the Anglican Church, which had "reformed" from the Catholic Church under Henry VIII, was as corrupt as its mother had been in the Middle Ages. In a much clearer way than we Americans today, they saw the dangers in fusing political and religious powers. While even the Deists in the group wanted to maintain the exercise of religious externalism, at the same time they wanted to avoid theocratic ideas taking hold, and turning the new Republic into what they had fought against.
Atheists like to paint all the Founders as Deists while some evangelical Christians view them as nearly religious fanatics. I think if we went back and time and saw what the Founders were really like, both groups would be sorely disappointed.
Suggested reading: http://www.economist.com/node/21541718
