Future Shock (tofler) or Shockwave Rider (brunner)
The Emperor's New Mind  (penrose)
A Brief History of Time (hawking)
Goedel Escher Bach (or Anything by hofstadter/Dennett)
The Minds Eye (H&D)
The Network Nation (Starr Roxanne Hiltz)
The Cuckoo's Egg (stoll)
The Mathematical Experience ( Philip J. Davis & Reuben Hersh (penguin 1981)
Surreal Numbers, (D.E. Knuth)
The Enigma, Alan Turing : the enigma / Andrew Hodges.
Wonderful Life (J Steve Gould)
The Selfish Gene (Dworkin)
Objective Knowledge (Popper)
Foucault's Pendulum (Umberto Eco)
Snowcrash, The Diamond Age and Cryptonomicon (Neal Stephonson)
Flatland (?)
On Human Communication (Cherry)
A Deepness in the Sky, Vernor Vinge,(isbn 1857988264)

Ian Stewart's books and Martin Gardner's books are all great fun.

Backnumbers of Scientific American - all the
- Computer Recreations columns and the maths things that came before
- those (mainly repeated in Gardner's books and Metamagical Themas, which
- is Hofstadter's compilation and extension of his SciAm columns- ). 
'The Soul of a New Machine'? (Hilary(?) Kidder)
 - about Data General's development of a
 - new mini-computer in record time etc etc - won a Pulitzer prize?
"the exploits of the incomparable mulla nasrudin."   
-  Sufi stuff could be regarded as having a place on the list.  
Zen & the Art of Motorcycle Maintenance (Pil?)
Life - A User's Manual (?)
"Chaos" by James Gleick (sp?)
The Computer and the Mind (P. Johnson-Laird)
Grammatical Man (J. Campbell - no relation)
The Sciences of the Artificial (H. Simon)
In the Age of the Smart Machine (S. Zuboff)
"Sphereland" (D. Burger).

The book by Hofstadter and Dennet is THE MIND'S I (Penguin).  The
authors say that anyone who confronts the questions 'What is the mind?',
'Who am I?', 'Can machines think?' runs headlong into perplexities which
they intend to reveal -- the book is designed to 'provoke, disturb and
befuddle its readers'.  I was certainly befuddled.

A v. good book by Hofstadter is METAMAGICAL THEMAS (a collection of
Scientific American articles written when H.  took over Martin
Gardner's 'Mathematical Games' column -- spot the anagram).  I think
it's now a Penguin paperback.  It has a lot of computer-related
material, including an exposition of LISP (and there's an extended
discussion of Rubik's Cube!).   And, of course, if only one book could
be chosen, it would have to be his GODEL: ESCHER: BACH.

The life of Turing is ALAN TURING:  THE ENIGMA by Andrew Hodges -- very
recommendable.   There is also CHARLES BABBAGE: PIONEER OF THE COMPUTER
(Oxford) by Anthony Hyman -- about a truly extraordinary man and his
struggles with Victorian-British anti-technological bias (not much
better today).

As a correction to the prevalent notion that computing originated
entirely in the US (and with IBM in particular), I recommend EARLY
BRITISH COMPUTERS by Simon Lavington (Manchester Univ Press p-b).
And dont't forget THINK: A BIOGRAPHY OF THE WATSONS AND IBM by William
Rodgers (Panther p-b), 

Someone mentioned THE EMPEROR'S NEW MIND:  CONCERNING COMPUTERS, MINDS,
AND THE LAWS OF PHYSICS by Roger Penrose (whose father, Prof Lionel
Penrose, was Professor of Eugenics (!) on the second floor of what is
now the UCL CS Department forty-odd years ago).   I found it rather
heavy going, and not altogether successful.

The 'Flatworld' book is FLATLAND by E A Abbott.   I can't find my copy,
but it is a shortish paperback.   It has, I believe, never been out of
print since its original publication in 1884.   Another book on a similar
theme is THE PLANIVERSE:  COMPUTER CONTACT WITH A TWO-DIMENSIONAL WORLD
(Picador) by A K Dewdney (Prof of CS and long-time Sci American columnist)
-- great fun.   He and his students designed and implemented a computer
model of a 2-D world -- and then, he says, it was 'invaded' by inhabitants
of a *real* 'planiverse'.

Two p-bs by William Poundstone are good.   One is THE RECURSIVE UNIVERSE:
COSMIC COMPLEXITY AND THE LIMITS OF SCIENTIFIC KNOWLEDGE (Oxford), which is
mainly about cellular automata, starting from Conway's 'Life'.   The other
is LABYRINTHS OF REASON:  PARADOX, PUZZLES AND THE FRAILTY OF KNOWLEDGE
(Penguin).

A recent book which I much enjoyed (and which provoked me into several
computer-graphical experiments -- it gives recipes) is COMPUTER PATTERN,
CHAOS, AND BEAUTY:  GRAPHICS FROM AN UNSEEN WORLD by C A Pickover (Sutton).

If I had to pick one book on the current state of Mathematics, it would be
THE PROBLEMS OF MATHEMATICS by Ian Stewart (Oxford p-b).   There is also
his DOES GOD PLAY DICE?  THE NEW MATHEMATICS OF CHAOS (Penguin).   And
James Gleick's CHAOS (now in p-b) is a good read.

There ought to be an elementary logic text:  either INTRODUCTION TO LOGIC
by Patrick Suppes (Van Nostrand) or the THE LANGUAGE OF LOGIC by Samuel
Guttenplan of Birkbeck College (Blackwell) would serve (both are p-bs). 
Suppes's book is a classic;  the other is more up-to-date:  it presents
propositional and predicate logic as languages which can be taught and
learnt by the 'direct method', as in modern teaching of foreign languages.

I'm looking forward to reading INFORMATION AND THE INTERNAL STRUCTURE OF
THE UNIVERSE (Springer-Verlag) by Tom Stonier, who is CS Prof at Bradford
(see review in Personal Computer World for May).   It appears to contend
that *information* is comparable with matter or energy as a fundamental
feature of the universe.


If you're including Physicsy books (as I take it you are with Hawkings BHoT)
then I recommend
	"What is Life ?", by E.Schrodinger (yes, the very same).

Highly readble treatment of the Statistical Thermodynamic arguement for Life
as Entropy reducing vector etc. Seems much neglected - I wonder if it is still
in print ?