Polls show that many voters would be disinclined to vote for an "atheist" for president. The most common explanation being that someone who isn't afraid of divine retribution can't be moral.
Most of these people would probably be surprised to know that they have elected many non-believers in the past. This is a guess about who these might have been in the recent past.
For most of the 19th and early 20th Century most white protestants (WASPs) practiced a type of conventional religion. They attended services regularly and professed all the standard responses about Christianity. There is only slight evidence as to how much this adherence to formal practice affected their day-to-day actions. The idea that a supernatural being doesn't exist was not something that arose in conversation very often.
There is some fairly strong evidence that the founders of the US were not conventional believers. This is usually covered by calling them "Deists". Jefferson is a good example. He removed all statements about the divinity of Jesus from a copy of his bible which left a picture of a moral philosopher rather than a religious figure. If there is a supernatural being according to this view he either doesn't meddle in the affairs of man, or has started the universe going and then stood aside to watch (the celestial clockmaker).
It seems probable that Franklin, Hamilton, Paine and a few others held similar views.
Many presidents up until the early part of the 20th Century were not called upon to discuss religion, so it is impossible to know their true feelings. Appeals to God in speeches and public statements are just conventions.
The last of these conventional Christian presidents may have been FDR. He doesn't have seemed to have invoked religious themes in his public life, but belonged to a mainline Protestant denomination and so nothing special was required of him to validate his religious views. Perhaps one could also include Truman in this mold as well, I'm not aware of any specific role that religion played in his life.
Eisenhower, another WASP, preferred golf to services, and never seems to have dealt with religious affairs. It is hard to be a general in wartime and still believe in the power of formal religion to do good, while people are slaughtering each other by the millions.
Kennedy, was a lapsed Catholic, which is why he had little trouble distancing himself from the church dogma. The public implicitly knew this as well which is why they believed him when he said he could keep religion out of his presidential decision making.
LBJ was too much of a scrapper and political operative to let religion enter into his life. Was he a "believer"? It is impossible to tell, but if actions speak louder than words then this didn't seem to be a topic of importance to him.
With Nixon we come to the first clear case of a non-believer. His Quaker background made so few claims on him that he was able to put it behind him early in his career. He was totally amoral, and not troubled by this.
Ford isn't worth discussing. His presidency was a place holder and he wasn't elected. Call him a conventional Christian if you insist on categorizing him.
Carter, as is well known, is a serious Christian and makes religion a basis for his life. His adherence to formal religion is so unusual compared to those before and after him that it just highlights how rare real religious belief among our recent presidents.
Reagan is the next clear example of a non-believer. In spite of his pandering to the religious right and injecting "God" into his pronouncements there is no indication that this was anything other than political pandering. He didn't attend services, claiming some sort of vague attendance at the Whitehouse. So the hero of the right was an atheist, his wife went so far as to get advice from astrologers.
George HW Bush, is a throwback to the mainline WASP who were the norm for office holders. Without any strong evidence lets call him conventionally religious.
Clinton is non-religious. I don't think he has ever spoken about the topic when he wasn't trying to score political points, so it is impossible to know exactly how he feels. Once again looking at his career it is clear that religion has played no part in his choice of actions and policies. As a highly educated and intelligent person it is unlikely that he adheres to any sort of traditional faith. I'd call him agnostic if I had to guess.
GW Bush is frequently claimed to be highly religious, but this is a misreading of him. He had some sort of "religious" epiphany which helped him overcome his alcoholism and he now adheres to some vague ideas that he adopted from this experience. This is not religion, it is a type of fetishism. He doesn't practice religion, doesn't attend services, and doesn't promote policies that the religious right thinks are important. He's not religious he's superstitious.
The current candidates:
McCain claims to be conventionally religious, but his performance before Rick Warren's church was a display of spouting religious cliche. His daily activities don't seem to indicate anything more that conventional WASP adherence. It is possible that he is agnostic, many people who have gone through personal trauma lose their simplistic faith.
Obama seems more involved in formal religion than most of those listed above. His attendance at an activist church and his long connection with the minister seems to indicate a serious involvement. He is probably as religious as most educated people get these days, aside from those who are members of various fringe sects and fundamentalist denominations.
So the score seems to be three, or possibly four, non-believers out of the past eleven presidents. This is about equal to the actual number of non-religious these days, estimated to be 30+% of the population. Apparently voters do trust atheists after all, they just don't want to think about it.