Many thanks to my friend (I'm not sure I should post names on this blog, so I'll just say he knows I'm talking about him, and that's good enough for me) who introduced me to the first two materials on this list, and generally owns me at philosophy.
(1): Godel, Escher, Bach: hands down the most provocative, interesting, best written (I believe), and one of the funniest, things I've read in my life ever. If you are a human being with any interest in mathematics and logic and philosophy, please do yourself a favor and pick this gem up. You won't regret it.
(2): Eliezer Yudkowsky's website: a fantastic and clear introduction to modern rational thinking (though I do disagree with him on a few points, namely the idea that if I 'woke up with a blue tentacle instead of my left arm', there would be nothing for a rational person to do - if I do, clearly I'm dreaming and will wake up with my left arm back, so there's your 'useful prediction,' Yudkowsky). Also contains very interesting ideas about technology (singularity for the win) and some very interesting pieces of fiction (notably "Three Worlds Collide").
(3): Watchmen: interesting, entertaining, beautifully drawn, with real atmosphere and one of the best scenes of all time (in my opinion) - the funeral scene where each attendee has a flashback of the Comedian. This book proves that "super-heroes" and comic-book format are not just for little kids (Watchmen is NOT for kids - this stuff would just go over their heads), and proves it spectacularly. Props to it for having NO traditional "bad guy" figures, with the exception of really minor characters (the only one I can think of is "Big Figure" and his goons - even the other retired super-villains are clearly human and (especially Moloch) just want to be left alone).
(4): Macchiavelli's "The Prince" and (to a slightly lesser extent) "Discourses on Livy": the first clear-headed political thinker and godfather of realpolitik gives us a real insight into human nature and the nature of governments.
(5): Raymond Smullyan's "To Mock a Mockingbird": I admit I couldn't push my way through this incredibly dense exercise in logic, but it is well written and anybody interested in a crash course in logic written in an interesting way should check it out.
(6): The Number Devil: Finally, an introduction for kids and math illiterates to what really makes mathematics interesting. None of that boring number crunching crap here - only genuinely interesting (albeit well-known to any mathematician) ideas. Continuing on this theme, I can recommend many casual-mathematics books as introductions to what real mathematicians do with their time, as well as the (totally non-textbook-style) textbook Winning Ways (Conway, Berlekamp, Guy), for anyone who ever wanted to beat someone else at a game.
(7): Blade Runner: yes, it's a movie, but that doesn't make it any less interesting (not to mention it's huge entertainment value). Watch it. It's good. In the same vein, watch District 9. Despite the obviousness of "the fluid" as a plot device, the movie is damn good, and will make you think.
(8): The Hitchhiker's Guide to the Galaxy: it's fucking hilarious. 'Nuff said.
(9): Logicomix. Deep, meaningful, insightful, and funny. Not an "intro to logic" (they tell you themselves in the opening pages), just the story of Bertrand Russell and the search for the foundations of logic.
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