“It is often stated that of all the theories proposed in this century, the silliest is quantum theory. In fact, some say that the only thing that quantum theory has going for it is that it is unquestionably correct.”

"Quantum Locality", Found Phys (2011) 41: 705–733

The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next (2007)

Bohr said this sentence in a conversation with Werner Heisenberg, as quoted in: "Der Teil und das Ganze. Gespräche im Umkreis der Atomphysik" . R. Piper & Co., München, 1969, S. 280. DIE ZEIT 22. Aug. 1969 http://www.zeit.de/1969/34/kein-chaos-aus-dem-nicht-wieder-ordnung-wuerde.
As quoted in Meeting the Universe Halfway (2007) by Karen Michelle Barad, p. 254 http://books.google.com/books?id=4qYorOpfB6EC&lpg=PP1&pg=PA254#v=onepage&q&f=false, with the quote attributed to The Philosophical Writings of Niels Bohr, but with no page number or volume number given.
David Mermin, on pages 186– 187 http://books.google.com/books?id=bf5bjBk095UC&lpg=PP1&pg=PA187#v=onepage&q&f=false of his book Boojums All the Way Through: Communicating Science in a Prosaic Age (1990) noted that he specifically looked for pithy quotes about quantum mechanics along these lines when reviewing the three volumes of The Philosophical Writings of Niels Bohr, but couldn't find any: <blockquote>Once I tried to teach some quantum mechanics to a class of law students, philosophers, and art historians. As an advertisement for the course I put together the most sensational quotations I could collect from the most authoritative practitioners of the subject. Heisenberg was a goldmine: “The concept of the objective reality of the elementary particles has thus evaporated…”; “the idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them … is impossible …” Feynman did his part too: “I think I can safely say that nobody understands quantum mechanics.” But I failed to turn up anything comparable in the writings of Bohr. Others attributed spectacular remarks to him, but he seemed to take pains to avoid any hint of the dramatic in his own writings. You don't pack them into your classroom with “The indivisibility of quantum phenomena finds its consequent expression in the circumstance that every definable subdivision would require a change of the experimental arrangement with the appearance of new individual phenomena,” or “the wider frame of complementarity directly expresses our position as regards the account of fundamental properties of matter presupposed in classical physical description but outside its scope.”<p>I was therefore on the lookout for nuggets when I sat down to review these three volumes – a reissue of Bohr's collected essays on the revolutionary epistemological character of the quantum theory and on the implications of that revolution for other scientific and non-scientific areas of endeavor (the originals first appeared in 1934, 1958, and 1963.) But the most radical statement I could find in all three books was this: "...physics is to be regarded not so much as the study of something a priori given, but rather as the development of methods for ordering and surveying human experience." No nuggets for the nonscientist.</blockquote>
Variants: Those who are not shocked when they first come across quantum mechanics cannot possibly have understood it.
Those who are not shocked when they first come across quantum theory cannot possibly have understood it.
Anyone who is not shocked by quantum theory has not understood a single word.
If you think you can talk about quantum theory without feeling dizzy, you haven't understood the first thing about it.

Interview in The Hindu (2013)
Context: The improved understanding of the equations of hydrodynamics is general in nature; it applies to all quantum field theories, including those like quantum chromodynamics that are of interest to real world experiments. I think this is a good (though minor) example of the impact of string theory on experiments. At our current stage of understanding of string theory, we can effectively do calculations only in particularly simple — particularly symmetric — theories. But we are able to analyse these theories very completely; do the calculations completely correctly. We can then use these calculations to test various general predictions about the behaviour of all quantum field theories. These expectations sometimes turn out to be incorrect. With the string calculations to guide you can then correct these predictions. The corrected general expectations then apply to all quantum field theories, not just those very symmetric ones that string theory is able to analyse in detail.

Lecture at the Amsterdam Symposium on Gravity, Black Holes, and String Theory (21 June 1997)

What Is Life? (1944)

Source: Information, The New Language of Science (2003), Chapter 25, Zeilingers Principle, Information at the root of reality, p. 231

Source: The Corporate Revolution in America, 1957, p. 287

Source: The Fabric of Reality (1997), Ch. 2
Context: The quantum theory of parallel universes is not the problem, it is the solution. It is not some troublesome, optional interpretation emerging from arcane theoretical considerations. It is the explanation—the only one that is tenable—of a remarkable and counter-intuitive reality.