As is traditional in such situations, I'm going to say it out that the books I like are better than the books you like so there.

I don't presume to know what the "best nonfiction books of all time*" (*in English) are but if I had to compile a list of the nonfiction books I've read that really made me feel like I was a better informed person for having read them, I'd say these would feature:

1) Friday Night Lights, HG Bissinger: A book that, for me, exploded my preconceptions about the state of race relations, education and sport in America from an English naivete to something more aware. A book I read not knowing anything about the sport it talked of, but which was more than merely a book about sport. Genuinely tragic and shocking at times, a book I never hesitate to recommend to others. I began reading it thinking that school sport, while something I hated, was something vital and important and that the fierce competition criticised by some leftist thinkers was good (a viewpoint I suppose is Nietzschean) - I finished reading it realising that what people like Chomsky say about the dangers of tribal sporting culture perhaps has more validity than I gave it credit for.

2) Ways of Seeing, John Berger: The book that, when I read it at university, made me realise that if you think studying popular or new media is a silly, worthless pursuit - or in some way a soft subject - you are quite simply wrong. A look at art that teaches the reader how to be visually literate, and encourages them to apply this to everything rather than just the "classics". In a time when there's a constant call for mass media and "geek" pursuits to be "taken seriously" it is by reading Berger and Barthes that people will be able to talk seriously about comics, games and television.

3) Practical Criticism, IA Richards: What Berger did for visual art for me, Richards did for literature. Not so much teaching me how to spot themes and techniques in the hoary old canon, but how to read in a way that makes every book more rewarding. There's something of a belief that "analysing" a book is antithetical to "enjoying" it. Reading about the elements of literary and cultural analysis made me realise, I think, that not only does being able to analyse make one able to enjoy things more deeply without consciously needing to sit down and write an essay about everything, knowing the theories of criticism let you articulate what you like about things all the more eloquently.

It's rather annoying that the books have to be in English, otherwise I would have suggested Sei Shonagon's Pillow Book as something I found immensely interesting.

I think that the work that Rebecca Solnit has done over the past decade is significant. There are a number of her books that could be recommended. Perhaps the one that inspires the most knee-jerk anger is MEN EXPLAIN THINGS TO ME.

Terry Tempest-Williams wrote a brilliant book called REFUGE. In it, she documented three things that turned out to have connections: her entire matrilineal line, going back three generations, of reproductive cancers. The flooding of the Great Salt Lake Basin. And, U.S. atomic bomb testing in the Nevada desert in the 1950s.
For those of us living in the west of the U.S. (from being a kid until I moved away at age 30), living out west sometimes feels the equivalent of living in the north of England (I'm originally from Manchester). The gov't treated us like guinea pigs.

I have others to suggest, but I know your list will soon get full.

What If by Randall Monroe. The author uses sound scientific principles to answer questions such as (and I probably paraphrase) 'What if I could throw a baseball at the speed of light?', in a very entertaining way.

The Empty Space by Peter Brook. A wonderful, virtually talismanic discourse on the power of theatre, that proves sometimes the best things come in small packages.

The Shock Doctrine by Naomi Klein. A dissection of global politics that devastatingly reveals the world as it really works.

Touching The Void, Joe Simpson's account of being left to die on the side of a remote Peruvian mountain with a shattered knee. After being stuck down a crevasse for days, he somehow found the drive to find a way out and crawl across glacier and moraine until, on the verge of death, he made it to the camp which his friends were about to vacate. It can be read as a straight mountaineering adventure story, and indeed it's one of the best I've ever read, but what makes it special is what it can say about the "indomitable human spirit" or whatever the phrase is. Gripping, reflective, and unforgettable.

May be a little low brow for some on here judging by the comments but I immensley enjoyed Bill Bryson's 'A History of Nearly Everything'.

Just the level of depth and gentle humour necessary to provide a great introduction to a whole range of subjects that you could then pursue further if they peak your interest.

Anyone wishing they knew a bit more about stuff generally (from gravity to alchemy to the origins of life), then I'd highly recommend it. Closest I've ever come to emailing an author to express my gratitude and admiration!

Undoubtedly Marc Bloch's Feudal Society. I have read many, many history books, and this one makes everything else look small and clumsy.

He describes medieval society piece by piece, with every new chapter revealing something new, fascinating and unexpected. It is incredibly erudite but entirely accessible to any interested reader. It definitely deserves its reputation.

That's pretty easy.

On the Origin of Species, by Charles Darwin, it not only shaped modern science, but also led to an entire new conception about what is to be a human.

A Treatise of Human Nature, by David Hume, one of the most relevant philosophical works of all times, that put most Western thinkers on guard to defend the knowledge against skepticism.

On Civil Disobedience, by Henry David Thoreau. It set the principles for many non-aggressive civil movements, ranging from Gandhi to Martin Luther King Jr.

1. Godel, Escher, Bach - Douglas R Hofstadter
2. QED: The Strange Theory of Light and Matter - Richard Feynman
3. Mythologies - Roland Barthes

1. An extraordinarily wide-ranging book which is at once mind-expanding yet accessible. Hofstadter attempts to explain one of the great theorems of modern mathematics in layman's terms, whilst finding many parallels between mathematics, music and art, and exploring such diverse topics as artificial intelligence, viruses, DNA and much more besides.

2. Quantum physics is never easy to grasp, but Feynman's little book is remarkably clear, and should be accessible to anyone with a reasonable grasp of high-school maths.

3. Barthes was wonderfully insightful on mid-20th century culture, media and advertising. He wrote these essays before he'd had much contact with the structuralists/post-structuralists, so (the last few chapters aside, which he wrote after Levi-Strauss suggested he read de Saussure) this book is refreshingly accessible and jargon-free. It is an original and brilliant mind at work, exploring areas that had hitherto been neglected, but play such an important role in how people think and act in our media-saturated world.