For aspiring programmers, we’d recommend the following books. (All affiliate commissions will be donated entirely to a local library.)

Software Engineering

• 
  Writing Solid Code
  Steve Maguire
  Microsoft Press, 1993
  Instructional

  [Note: Probably a bit dated and C/C++ specific now.]

• 
  Programming C# 3.0
  Jesse Liberty, Donald Xie
  O’Reilly Media, 2007
  Instructional

• 
  Code Complete
  Steve McConnell
  Microsoft Press, 2004
  Instructional

• 
  The Pragmatic Programmer
  Andrew Hunt, David Thomas
  Addison Wesley, 1999
  Instructional

• 
  Refactoring
  Martin Fowler, Kent Beck, et al
  Addison Wesley, 1999
  Reference

• 
  Design Patterns
  Erich Gamma, Richard Helm, et al
  Addison Wesley, 1995
  Reference

C++

• 
  The C++ Programming Language
  Bjarne Stroustrup
  Addison Wesley, 1997
  Instructional

• 
  The C++ Standard Library
  Nicolai Josuttis
  Addison Wesley, 1999
  Instructional

• 
  Effective C++
  Scott Meyers
  Addison Wesley, 2005
  Instructional

• 
  More Effective C++
  Scott Meyers
  Addison Wesley, 1996
  Instructional

• 
  Exceptional C++
  Herb Sutter
  Addison Wesley, 1999
  Instructional

• 
  Modern C++ Design
  Andrei Alexandrescu, Scott Meyers, et al
  Addison Wesley, 2001
  Instructional

  [Note: Fairly hardcore template programming. Read this last!]

• 
  C++ Coding Standards
  Herb Sutter
  Addison Wesley, 2004
  Instructional

Other Languages (For the true language geek)

• 
  The Little Schemer
  DP Friedman
  MIT Press, 1996
  Instructional

• 
  Structure and Interpretation of Computer Programs
  Harold Abelson, Gerald Jay Sussman
  MIT Press, 1996
  Instructional

  [Note: Read it free online. Also check out the video lectures.]

• 
  The ANSI Common Lisp Book
  Paul Graham
  Alan Apt, 1995
  Instructional

• 
  Purely Functional Data Structures
  Chris Okasaki
  Cambridge University Press, 2008
  Instructional

• 
  Programming in Lua
  Roberto Ierusalimschy
  Lua.org, 2006
  Instructional

Core Computer Science Topics

• 
  Introduction to Algorithms
  TH Cormen
  MIT Press, 2001
  Instructional

• 
  Compilers: Principles, Techniques and Tools
  Alfred Aho, Monica Lam, et al
  Addison Wesley, 2006
  Instructional

• 
  Algorithms
  Robert Sedgewick
  Addison Wesley, 1988
  Reference

  [Note: A classic from 1988. There are newer versions in more modern languages but the original Pascal one is fine.]

Pure Classics

• 
  The Mythical Man-Month
  Frederick Brooks Jr.
  Addison Wesley, 1995
  Instructional

• 
  Peopleware
  Tom DeMarco
  Dorset House, 1999
  Instructional

• 
  Programming Pearls
  Jon Bentley
  Addison Wesley, 1999
  Instructional

Software Development Process

• 
  Agile Software Development with SCRUM
  Ken Schwaber, Mike Beedle
  Prentice Hall, 2002
  Instructional

• 
  Extreme Programming Explained
  Kent Beck
  Addison Wesley, 2004
  Instructional

• 
  Rapid Development
  Steve McConnell
  Microsoft Press, 1996
  Instructional

Mathematics

• 
  Matrix Computations
  Gene Golub, Charles Van Loan
  Johns Hopkins University Press, 1989
  Instructional

• 
  Computational Geometry in C
  Joseph O’Rourke
  Cambridge University Press, 1998
  Instructional

• 
  Numerical Recipes in C
  William Press, Brian Flannery, et al
  Cambridge University Press, 1992
  Reference

• 
  Numerical Linear Algebra
  Lloyd Trefethen
  Society for Industrial Mathematics, 1997
  Reference

Rendering and Animation

• 
  Computer Animation: Algorithms and Techniques
  Rick Parent
  Morgan Kaufmann, 2001
  Instructional

  [Note: The definitive book on algorithms for skeletal animation.]

• 
  Real-time Rendering
  Tomas Akenine-Moeller
  A K Peters, 2002
  Instructional

Threading and Concurrency

• 
  Patterns for Parallel Programming
  Timothy Mattson
  Addison Wesley, 2004
  Instructional

Networking

• 
  Illustrated TCP/IP
  Matthew Naugle
  John Wiley & Sons, 1998
  Instructional

• 
  Cisco CCNA Exam Certification Library
  Wendell Odom
  Cisco Press, 2007
  Instructional

  [Note: Surprisingly good for a vendor-specific guide. Gives a good explanation of TCP/IP basics.]

Artificial Intelligence

• 
  Artificial Intelligence
  Stuart Russell, Peter Norvig
  Pearson Education, 2003
  Instructional

• 
  AI Game Programming Wisdom
  Steve Rabin
  Charles River Media, 2002
  Reference

• 
  AI Game Programming Wisdom 2
  Steve Rabin
  Charles River Media, 2003
  Reference

• 
  AI Game Programming Wisdom 3
  Steve Rabin
  Charles River Media, 2006
  Reference

• 
  AI Game Programming Wisdom 4
  Steve Rabin
  Delmar, 2008
  Reference

Test Engineering

• 
  Pragmatic Unit Testing in C# with NUnit
  Andy Hunt, Dave Thomas, et al
  Pragmatic Bookshelf, 2007
  Instructional

  [Note: Not the best book, and some of the code examples leave a lot to be desired, but the fundamentals are still there and quite well explained.]

• 
  xUnit Test Patterns: Refactoring Test Code
  Gerard Meszaros
  Addison Wesley, 2007
  Reference

  [Note: Everyone should use this for any large-scale test framework design.]