I recently re-read Roger Penrose's The Emperor's New Mind. I read it first in 1990, soon after it came out, and I still find it a stunning book, despite disagreeing with Penrose's speculations about consciousness somehow being boosted by quantum effect.
What makes the book so great in my view is that, in order to make his point, he has written an incredibly accessible textbook about a large number of topics in mathematics, physics and computer science. Penrose doesn't dumb down anything: he assumes the reader is an intelligent layperson, and explains each topic without compromise (though without getting into the technicalities of proofs).
Mathematical/computer topics include the theories of computability and algorithm complexity, Gödel's theorem, the Mandelbrot set, Turing machines (there's an appending with several pages of ones and zeros encoding a universal Turing machine -- I haven't checked it, but I'm sure that Penrose did), the Church-Turing thesis, and so on. In physics, he explains Maxwell's theory of electromagnetism (this was the first time I understood it), Phase space, special and general relativity, quantum theory, cosmology, black holes, space-time singularities and more. The table of contents reads like an overview of modern "hard" science. In the mean time Penrose also manages to explain Penrose tiling (the nonperiodic tiling of the plane, which he invented in the 1970s), the physics of nerve signals, Platonism, and important topics from the modern history of mathematics like Hilbert's program and Bertrand Russel's Principia Mathematica.
It's not surprising that Penrose shows prominently in the acknowledgments for Neil Stephenson's novel Anathem (in fact finding it there made me pick up my copy and start re-reading it).
Despite all this, I disagree with Penrose's claims about consciousness. Penrose does a good job separating his opinions on this topic from the science he presents, and in the end he cannot prove his hunches about consciousness any more than I can mine. Personally, I think that evolution is a perfectly fine explanation for our brains -- in other words, Richard Dawkins did a better job convincing me than Penrose. (I cannot recommend Dawkins' books enough -- you can skip The God Delusion though, just stick to his many excellent works about evolution and memes.)