“The United States appear to be destined by Providence to plague America with misery in the name of liberty.”

Speech to the Constitutional Club (20 November 1923), quoted in The Times (21 November 1923), p. 17

2015, State of the Union Address (January 2015)
Context: You know, just over a decade ago, I gave a speech in Boston where I said there wasn’t a liberal America or a conservative America; a black America or a white America -- but a United States of America.



Context: There is not a liberal America and a conservative America — there is the United States of America. There is not a Black America and a White America and Latino America and Asian America — there's the United States of America.

Source: Artefactos

1970s, Proclamation 4417 (1976)

Attributed to Washington in "Farewell to the United States of Europe: long live the EU!" by André Fontaine at Open Democracy (29 November 2001) http://www.opendemocracy.net/democracy-europefuture/article_344.jsp. It appears to have originally circulated in French:
:: Je suis citoyen de la Grande République de l'Humanité. Je vois le genre humain uni comme une grande famille par des liens fraternels. Nous avons jeté une semence de liberté et d'union qui germera peu à peu dans toute la Terre. Un jour, sur le modèle des Etats-Unis d'Amérique, se constitueront les États-Unis d'Europe. Les États-Unis seront le législateur de toutes les nationalités.
: An anonymous blogger in "Did George Washington predict a "United States of Europe"? (30 January 2010) http://racehist.blogspot.com/2010/01/did-george-washington-predict-united.html showed that it derived from Gustave Rodrigues, Le peuple de l'action: essai sur l'idéalisme américain (A. Colin, 1917), p. 207:
:: Washington écrivait à La Fayette qu'il se condérait comme « citoyen de la grande république de l'humanité » et ajoutait : « Je vois le genre humain uni comme une grande famille par des liens fraternels ». Ailleurs il écrivait, prophétiquement: « Nous avons jeté une semence de liberté et d'union qui germera peu à peu dans toute la terre. Un jour, sur le modèle des Etats-Unis d'Amérique, se constitueront les États-Unis d'Europe. »
: A translation by Louise Seymour Houghton ( The People of Action: An Essay on American Idealism (1918) http://books.google.com/books?id=b8Y9AAAAYAAJ) reads:
:: Washington wrote to Lafayette that he considered himself a "citizen of the great republic of humanity," adding: "I see the human race a great family, united by fraternal bonds." Elsewhere he wrote prophetically: "We have sown a seed of liberty and union that will gradually germinate throughout the earth. Some day, on the model of the United States of America, will be constituted the United States of Europe." [pp. 209-210]
: The first two quotations come from a letter to the Marquis de Lafayette of 15 August 1786 (see above) as quoted in Joseph Fabre's Washington, libérateur de l'Amérique: suivi de Washington et la revolution Américaine (Ch. Delagrave, 1886), and the third is also found in that source where, although placed between quotation marks, it is clearly intended as the author's own comments on what "Washington and his friends" were saying to the world by establishing the American Constitution. Gustave Rodrigues mistakenly printed Fabre's words as Washington's alongside some actual observations of his from a letter to Lafayette, and so created the misquotation.
Misattributed

Presidential declaration speech, Ted Cruz declaration speech: Full transcript http://www.independent.co.uk/news/world/americas/ted-cruz-declaration-speech-full-transcript-10128614.html, Independant.co.uk (March 23, 2015)
2010s

On Revolutionary Medicine (1960)

BuzzFlash interview (2004)