Some good suggestions (and a couple I'll have to read...) I'd add the following:
8. "The Mythical Man-Month" by Fred Brooks (still, IMO, one of the best management books ever, esp. for software and product development.)
9. Boyd: The Fighter Pilot Who Changed the Art of War
by Robert Coram (OODA is the true core of agile thinking, and it works pretty much everywhere.)
For software and computers specifically, add:
10. Computer Lib/Dream Machines by Ted Nelson (Impossible to categorize - it's a hypertext book for crying out loud - but browsing it can change your thinking.)
11. The Soul of a New Machine by Tracy Kidder. (Good for new products in general.)
And for general management and leadership inspiration, two great autobiographies:
12. Mover of Men and Mountains, by R.G. Le Tourneau.
13. Rickenbacker, by Eddie Rickenbacker.