When I was younger some of my favorite books were Raymond Smullyan's puzzle books. He strove to write books that covered topics more deep than more standard children's puzzles; To Mock a Mockingbird gets into serious thought about combinatory logic, and Forever Undecided, an introduction to Godel's incompleteness theorem, phrasing everything in terms of the classic children's puzzles about people who always lie and people who always tell the truth. (For a much shorter but higher-brow sample of what the writing looks like, he has a brief note about roughly the same subject.) I recently looked at them again, and they still hold up (or maybe are even made better) looking back at them with an actual math education.
What I would like are books that are accessible to a general audience - especially kids! - that nonetheless are able to introduce one to nontrivial, deep mathematics, like Smullyan's books above. I would prefer books that actually teach the mathematics (however disguised) as opposed to something like Simon Singh's expository book on Fermat's Last Theorem (which tells you the story of FLT, but nothing about the mathematics behind it.)