The Information by James Gleick certainly fits in that category. It tickled the Hofstadter part of my brain that had remained dormant for quite a while. Years ago in college I read and quickly became obsessed with Douglas Hofstadter's Godel, Escher, Bach: An Eternal Golden Braid. I was a math major in college, and I have to say that those first two years of the major were really an exciting time for me because my eye was opened up to so many beautiful ideas, everything from the strange new field of Graph Theory to the centuries-old, strange and abstract field of Real Analysis. To see the ideas of mathematics applied to theories of consciousness in Gödel was truly captivating. (Of course, I later drifted away from math precisely for the lack of applications, but for a while there, math had me sold and, alas, I stuck with the major throughout college.)
But what I liked about Gödel, in particular, was Hofstadter's style of presentation and his ultimate thesis, i.e., that the human mind is something quite different from a computer. The book, in conjunction with the followup, titled I Am a Strange Loop, stressed the ways in which humanity's search for meaning through analogy, and the ways in which we struggle with self-reference when interpreting meaning. It was really fascinating to see Gödel's theorem applied here: Gödel said that formal systems (say, something which might represent a computer) will necessarily contain theorems which, while true, are unprovable using the formal system's tools. He essentially constructed a sentence that talked about itself, using the language of that very formal system. So that was dubbed "incompleteness" and Hofstadter uses the idea of incompleteness and of self-reference to say that it represents human consciousness, more or less. (Try answering the question, "why do you love your favorite piece of music?" you find yourself stuck at some point without being able to come up with a reason other than "I just love it!")
At any rate, the reason I went into that long explanation is to say that Gleick's book comes to the completely opposite conclusion. He starts from the bottom up, from our DNA, and argues that we're just carriers of information. Furthermore, he does it in a very strange way. He spends a lot of time talking about the history of information transferal, essentially tracing the development of modern communication theory, and then talks about genetics toward the end. Don't get me wrong, that part of the text is really well done and I learned a lot about the practical problems faced by a lot of the information theorists. But, the story is all about figuring out how to mechanically transmit information. Little is mentioned about meaning, because Gleick's thesis is that humans are simply agents carrying information, so that the information is the true protagonist of the story, so to speak. Information, measured in the omnipresent "bit", defined the beginning of time and information will remain when we are extinct.
He basically flips Hofstadter's ideas on their head by saying that meaning is not the important point; it's about the ever-growing industry of data storage and how efficiently it can flow. Think Facebook, Google. I'm not enthusiastic about such a position; it doesn't get my juices flowing like Hofstadter's book does. And I would say that Hofstadter provides a much better written and compelling case for his point of view. Gleick's story involves a lot of discussion of the brilliant inventor, and the development of communication technology is obviously related to military, development of the state, and private interests -- so how can there not be any discussion of meaning/symbols of information theory? Information technology is controlled, distorted, and manipulated constantly, so meaning inevitably "creeps in" wherever you talk about information even how it flows and is manufactured. And I'm sure Gleick would even agree with this statement. But the book is completely unconcerned with any of these ideas.
So whereas in Hofstadter I see a real concern with skepticism and philosophical concerns, Gleick's The Information is too dry. I wished there were more discussion of the humanity of it all, but I accept that perhaps that task is too much to tackle in a book which is already 400+ pages. Still, it didn't captivate me the way Hofstadter did and I think that derives from the somewhat flat conclusion and the (at times) slow pacing of the text.
An interesting exercise might be to think about how the incompleteness theorem could be applied to economics. It's already been applied to many different areas of science and philosophy, and I'm sure if someone wrote a pop-econ piece on it it would garner at least some widespread attention. The problem is that it's not exactly a mainstream idea: the thought that individuals are not soulless utility computers might cause most economist's heads to explode. The idea that there exists a human consciousness which, at its core, cannot be modeled formally, might risk a lot of Harvard tenured positions.