“Religion, which should most distinguish us from the beasts, and ought most particularly elevate us, as rational creatures, above brutes, is that wherein men often appear most irrational, and more senseless than beasts.”

XX. On Transmigration of Souls, and how Souls are said to migrate into brute beasts.
On the Gods and the Cosmos

“I do.”
Source: The Man in the Maze (1969), Chapter 8 (p. 118)

Part 3, Section 16
A Treatise of Human Nature (1739-40), Book 1: Of the understanding

Letter to Edward Newenham (20 October 1792) http://etext.lib.virginia.edu/etcbin/toccer-new2?id=WasFi32.xml&images=images/modeng&data=/texts/english/modeng/parsed&tag=public&part=155&division=div1, these statements and one from a previous letter to Newenham seem to have become combined and altered into a misquotation of Washington's original statements to read:
1790s
Context: Of all the animosities which have existed among mankind, those which are caused by difference of sentiments in religion appear to be the most inveterate and distressing, and ought most to be deprecated. I was in hopes that the enlightened and liberal policy, which has marked the present age, would at least have reconciled Christians of every denomination so far that we should never again see the religious disputes carried to such a pitch as to endanger the peace of society.

The Education of Women (1719)

30 August 1833
Table Talk (1821–1834)

Statement of 1864, quoted in Pamphlets on the Deaf, Dumb & Blind http://books.google.com/books?id=FLcMAQAAIAAJ&q=%22There+is+no+dress+which+embellishes+the+body+more+than+science+does+the+mind%22&dq=%22There+is+no+dress+which+embellishes+the+body+more+than+science+does+the+mind%22&hl=en&sa=X&ei=UlFgVOWoJY-uyATH1YDACQ&ved=0CB8Q6AEwAA

Texts and Pretexts (1932), p. 270
Context: It is man's intelligence that makes him so often behave more stupidly than the beasts. … Man is impelled to invent theories to account for what happens in the world. Unfortunately, he is not quite intelligent enough, in most cases, to find correct explanations. So that when he acts on his theories, he behaves very often like a lunatic. Thus, no animal is clever enough, when there is a drought, to imagine that the rain is being withheld by evil spirits, or as punishment for its transgressions. Therefore you never see animals going through the absurd and often horrible fooleries of magic and religion. No horse, for example would kill one of its foals to make the wind change direction. Dogs do not ritually urinate in the hope of persuading heaven to do the same and send down rain. Asses do not bray a liturgy to cloudless skies. Nor do cats attempt, by abstinence from cat's meat, to wheedle the feline spirits into benevolence. Only man behaves with such gratuitous folly. It is the price he has to pay for being intelligent but not, as yet, intelligent enough.