https://www.amazon.com/CYBERPUNK-Outlaws-Hackers-Computer-Fr...
Others have listed some great, entertaining reads already:
Hackers,
Soul Of A New Machine (which won a Pulitzer),
Cringley's PBS series Triumph Of The Nerds (available on YouTube),
Where Wizards Stay Up Late
Some not mentioned so far (as I write):
The ancient, online Jargon File is a large glossary that captures a lot of early computer subculture through its lexicon. Eric S. Raymond maintains it today, but it originated way back in the 1970s: http://www.catb.org/jargon/html/
"American Experience," on PBS, did a stellar documentary on the origins of Silicon Valley and the pervasive startup mentality there. It's all about the rise of the semiconductor industry, starting with transistors. Watch online: http://www.pbs.org/wgbh/americanexperience/films/silicon/
Dropping LSD was, it turns out, crucial to the origins of personal computing! This I learned from Jaron Lanier and Kevin Kelly, who recommended John Markoff's What The Dormouse Said: http://www.amazon.com/What-Dormouse-Said-Personal-Computer-e...
The Difference Engine: Charles Babbage and the Quest to Build the First Computer is a short book but also a fun read. Doron Swade, technology historian and assistant director of London's Science Museum, races to build a copy of Charles Babbage's "difference engine" before the anniversary of said machine; he tells his travails in building it while giving Charles Babbage's story at the same time: http://www.amazon.com/Difference-Engine-Charles-Babbage-Comp...
No one has mentioned books covering the dark side of hacking. There are some great reads out there, and infosec is a crucial part of computer history.
CYBERPUNK: Outlaws and Hackers on the Computer Frontier covers Kevin Mitnick, the Chaos Computer Club, and Robert Tappin Morris (who, somewhat inadvertently, wrote the first Internet worm). Mitnick disputes his section of the book, but it's fascinating nonetheless. Worth it for the Morris part alone: http://www.amazon.com/CYBERPUNK-Outlaws-Hackers-Computer-Fro...
The Cuckoo's Egg: Tracking a Spy Through the Maze of Computer Espionage by Clifford Stoll is a fun read. Stoll is an astronomer by trade, and his analytical thinking can be an inspiration: http://www.amazon.com/The-Cuckoos-Egg-Tracking-Espionage/dp/...
The Watchman is a true crime thriller you won't be able to put down. The author set out to write a book on Mitnick but wound up detouring to do a story on Kevin Poulsen, who is now an excellent infosec writer at Wired. You will not believe what Poulsen does in this book. http://www.amazon.com/Watchman-Twisted-Crimes-Serial-Poulsen...
The Hacker Crackdown by acclaimed sci fi author Bruce Sterling is a great work on an infamous cross-country bust of many hackers. You'll get a look into the BBS subculture, Phrack Magazine, and the phreaker scene. http://www.amazon.com/Hacker-Crackdown-Disorder-Electronic-F...?
And let's not forget gaming:
Masters of Doom: How Two Guys Created an Empire and Transformed Pop Culture gives a great history of ID Software and the origins of the FPS: http://www.amazon.com/Masters-Doom-Created-Transformed-Cultu...
Read a book that had a section on him (and pg) written before they founded Viaweb. http://www.amazon.com/CYBERPUNK-Outlaws-Hackers-Computer-Fro...
Also, there are two Robert Morris, rtm, and his dad who also has a wikipedia article http://en.wikipedia.org/wiki/Robert_Morris_%28cryptographer%...
[1]: http://www.amazon.com/CYBERPUNK-Outlaws-Hackers-Computer-Fro...
This book was really my entry point into the world of "hacking" as "breaking into things" and computer security, and the computer underground scene. It's broken into three sections:
1. A recounting of Kevin Mitnick's early days out in LA
2. A stripped down re-telling of the German hackers story (as recounted at greater length and in first-person in The Cuckoo's Egg)
3. A section on Robert Morris and the "Morris Worm" events
There are some questions about the veracity of parts of this book, especially the sections on Mitnick, but I think it's still worth a read. But if you're into this sort of thing, I'd suggest also reading other books on Mitnick (particularly his auto-biographical book Ghost In The Wires[2]) to get a more balanced view of his story - as well as more of what happened later in Mitnick's life.
[1]: https://www.amazon.com/CYBERPUNK-Outlaws-Hackers-Computer-Fr...
[2]: https://www.amazon.com/Ghost-Wires-Adventures-Worlds-Wanted/...*