I don't usually like these types of big list questions, but I think this is actually fairly important as far as education, informing the public about what we do, and getting people excited about math goes. There were some pop math books that exposed me to great ideas and essentially made me want to become a mathematician.
For some examples of what I mean by "pop math" see this or this post.
What circle of ideas, biography of a mathematician, conjecture, or subject would you like to see as a popular math book for non-mathematicians?
Answers might be in the form of a theoretical title plus a brief description. For example,
Bezout's Theorem: a history of how the quest to understand how two curves intersect led to the birth of modern algebraic geometry.
There's room for a really well done biography of von Neumann. The one by MacRae is ok, but not great.
Peter Lax described von Neumann as possessing the "most scintillating intellect of this century."
Von Neumann was the first to rigorously establish a mathematical framework for quantum mechanics. He played a key role in inventing the computer. He invented game theory, and later used ideas from game theory in advising US officials at the highest level during the cold war. He is credited with the equilibrium strategy of mutually assured destruction, providing the deliberately humorous acronym, MAD.
There's ample material for biographies here.
Edit: A new biography called The Man from the Future: The Visionary Life of John von Neumann by Ananyo Bhattacharya has been published.