StackOverflow recently voted on the "most influential programming book". The Internet Security Blog brings a neatly formatted list. Finally, the question was repeated on Slashdot; which is of course like asking a class of ten year olds about their favourite bubble gum. Surprisingly, some interesting information could be extracted from the noise.

The top ten:

Code Complete (2nd Edition)
The Pragmatic Programmer: From Journeyman to Master
Structure and Interpretation of Computer Programs (2nd ed.)
The C Programming Language (2nd ed.)
Introduction to Algorithms
Refactoring: Improving the Design of Existing Code
Design Patterns: Elements of Reusable Object-Oriented Software
The Mythical Man-Month: Essays on Software Engineering
Art of Computer Programming, Volume 1: Fundamental Algorithms (3rd Edition)
Compilers: Principles, Techniques, and Tools (2nd Edition)

Other

The C Programming Language
Design Patterns
Deitel & Deitel
The Mythical Man-Month
John von Neumann: Theory of self-reproducing automata
The Art of Unix Programming
Starting Forth by Leo Brodie
Peter Norton's Guide to Programming the IBM PC
Bruce Eckel's Using C++ and Thinking in C++
The Design of Everyday Things by Donald Norman
Algorithms + Data Structures = Programs by Niklaus Wirth

And there's even more.