These are books that I found worth reading as background or for alternate views, or just because they were interesting. No particular order.
How to Lie with Statistics, Darrell Huff, Norton, 1954 (reissued in 1993). A wonderful little book that will immunize you for a lifetime against statistical chicanery and meaningless numerical presentations.
The Victorian Internet: The Remarkable Story of the Telegraph and the Nineteenth Century's On-Line Pioneers, Tom Standage. Walker & Co, 1998. (Paperback coming soon, it is said.) Fascinating story of the development and spread of a new technology and its effects in society; the parallels with today's Internet are many.
The Early History of Data Networks, Gerard Holzmann, Bjorn Pehrson IEEE Press, 1994. (I'm biased, since the first author is a good friend.) A more scholarly but still interesting description of the optical telegraph, which 50 years before the "Victorian Internet" encountered many of the same issues and had some similar effects on society.
Many of the technical and social issues seen in today's Internet showed up in earlier networks, notably the telegraph network (Standage) and the optical telegraph networks of 50 years earlier (Holzmann). Among the topics: coding, error detection and recovery, privacy and security, spies and cryptography, bandwidth, congestion, money and speculation, social change, and ultimately, the end as something better comes along. The optical telegraph was killed by the electrical, which in turn was killed by the telephone.
The Pattern in the Stone: The Simple Ideas That Make Computers Work, Danny Hillis, Basic Books, 1998. A wonderfully evocative title, and a good attempt to explain how computers work. Hillis is a computer architect, founder of the now-defunct Thinking Machines Corp, which made highly parallel computers, and a very creative person. The book has some fascinating stories (my favorite is the computer in every hotel doorknob) and reasonable descriptions of And, Or, Not, and how they can be used, with plumbing and mechanical analogies. Some minor errors in description and illustrations. Some short essays on artificial intelligence, parallel computing, neural nets, etc. It's too much hardware, at too low a level, then too sweeping and vague, but interesting nevertheless.
ENIAC: The Triumphs and Tragedies of the World's First Computer, Scott McCartney, Walker & Company, 1999. Compact description of the invention of the first stored program computer (not invented by von Neumann, a case made fairly compellingly by the author). Surprisingly, he omits any mention of the work of Konrad Zuse in Germany.
Dealers of Lightning: Xerox PARC and the Dawn of the Computer Age, Michael A. Hiltzik, Harper, 1999. A very detailed look at how Xerox's Palo Alto Research Center invented many of today's basic technologies -- personal computers, bitmap displays, grpahical user interfaces, the Ethernet, the laser printer -- and how Xerox managed to capitalize on only one. Careful fact-checking, according to my source.
Show-Stopper! The Breakneck Race to Create Windows NT and the Next Generation at Microsoft, Pascal Zachary, Free Press, 1994. Vivid description of life in a large software project. It's now five years later, and things are not getting simpler.
I Sing the Body Electronic: A Year With Microsoft on the Multimedia Frontier, Fred Moody, Penguin, 1996. Another life-inside-Microsoft book, just as remarkable in its way as Zachary's story.
Burn Rate: How I Survived the Gold Rush Years on the Internet, Michael Wolff, Simon & Schuster, 1998. Success and ultimate failure in starting a Web business, with lots of nasty jabs at people he worked with. More interesting than most, and better written.
Web Security & Commerce, Simson Garfinkel & Gene Spafford, O'Reilly, 1997. The level is a bit erratic, but much of it should be accessible to non-experts.