Here are some books that I believe should be on every programmer's bookshelf.
"The C Programming Language, 2nd Edition
" - By the creators of the C language, this concise book clearly teaches the foundations for the C language. For a more tutorial book on C, I would suggest "C Primer Plus"
"Wiley's Teach Yourself C++
" by Al Stevens - My favorite book for learning C++.
"Programming Pearls " - A great collection of essays on programming including ways to approach programming problems.
"Programming Perl" - The definitive book for the Perl language by the creator of the language.
"The Art of Computer Programming, Volumes 1-4A Boxed Set
" - This thick 4 volume set is a thick academic tomb of knowledge for computer science.
" or "Software Tools in Pascal
" - Writing software tools and utilities is a special discipline.
"The Practice of Programming" - Easy to read text on programming practices.
"Win32 Programming" by Brent E. Rector, Joseph M. Newcomer - While Petzold's Programming Windows®, Fifth Edition is generally considered THE book on windows programming, I actually like this book better because of its more in-depth coverage of the topics.
Here are some books for the professional programmer that isn't around coding.