The top two definitions there seem to sugest that deism was especially popular amongst the FF’s. Why was that?
It’s popularity wasn’t exclusive to them. It was an outgrowth of the European “Age of Enlightenment”, and was professed by many progressive European thinkers of the day. The American founding fathers were influenced heavily by enlightenment philosophers such as Locke, Rousseau, and Voltaire.
I don’t know if I’d call it “especially popular” among the founding fathers, but a number of notable founding fathers were Deist. But, like yabob said, it was a popular philosophy among English and French intellectuals at the time, because it tried to reconcile rationalism and faith, science and religion.
An idea from the Age of Enlightenment was to discard your preconceived notions, and look at evidence and reason. Since there was no evidence that a god was at work in the workings of the world, but it was apparently created by something (else where did everything come from?), Deism was a natural outcome.
Of course, since then, the notion that the world must have a creator is no longer required, since the Big Band and evolution do a pretty good job of explaining that part. Deists in the 18th century were the equivalent of today’s atheists. IMHO they would have been atheists had they had access to the works of Darwin and modern astrnomers.
s/Big Band/Big Bang’;
Many of the founding fathers lived in a time when thermodynamics, mechanics, etc. were beginning to make it obvious that the universe didn’t need a constantly present God to make things run, that the laws of physics could keep everything going well. Comparing the universe to a “clockwork” and such was a popular metaphor to demonstrate how, once a creator was done with the original creating, the simpilist, most perfect (and therefore most likely) thing for him to have done was to let it run without his interference. As a bunch of intellectuals, and in several cases scientists, the founders were more aware of these ideas and developments then the more pious general American public.
Indeed Thomas Jefferson was often accused of being an athiest because of his deism.
The usual example I hear of deism amonst the founders was Thomas Jefferson. I think Thomas Paine was a straight up atheist. Does anyone know what other Founding Fathers were
Oh, I don’t know, there’s something kind of appealing about the idea of the universe dripping out of the spit valve of the second saxaphone’s instrument. 
The Selfish Gene Krupa?
Or, as he put it:
In his Autobiography, Benjamin Franklin is very explicit about his Deism.
There’s some evidence George Washington was, though I don’t think he ever explictly stated it.