Edit: The book has lots of historical details about competing early technologies such as the OSI vs TCP/IP, C vs well-structured languages, Archie/WAIS/Gopher, attempts from different parts of the world such as AlohaNet in Hawaii and Minitel in France. That's just a sampler, but the story telling does not get too bogged down with too much details and moves along at a quick pace.
In all seriousness, Where the wizards stay up late (http://www.amazon.com/Where-Wizards-Stay-Up-Late/dp/06848326...) gives a good account of the beginning of the net. For the web there is How the web was born (http://www.amazon.com/How-Web-was-Born-Story/dp/0192862073/r...)
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