These are books considered most influential for programmers from this StackOverflow thread.

Cause SO is cathedral, Github is bazzar ;)

Long answer: I frequently visit above thread. Over the time, such an active thread is closed, links to book sites are removed and I have to copy/paste/search everytime I go there. I am afraid they might remove it entirely.

So, the list is preserved here :)

1. Code Complete (2nd edition) by Steve McConnell
2. The Pragmatic Programmer by Andrew Hunt and David Thomas
3. Structure and Interpretation of Computer Programs by Sussman and Abelson (free ebook)
4. The C Programming Language by Brian Kernighan and Dennis Ritchie
5. Introduction to Algorithms by Cormen, Leiserson, Rivest & Stein
6. Design Patterns by the Gang of Four
7. Refactoring: Improving the Design of Existing Code by Martin Fowler
8. The Mythical Man Month by Fred Brooks
9. The Art of Computer Programming by Donald Knuth
10. Compilers: Principles, Techniques and Tools by Alfred V. Aho, Ravi Sethi and Jeffrey D. Ullman
11. Gödel, Escher, Bach by Douglas Hofstadter
12. Clean Code: A Handbook of Agile Software Craftsmanship by Robert C. Martin
13. Effective C++ by Scott Meyers
14. More Effective C++ by Scott Meyers
15. CODE by Charles Petzold
16. Programming Pearls by Jon Bentley
17. Working Effectively with Legacy Code by Michael C. Feathers
18. Peopleware by Demarco and Lister
19. Coders at Work by Peter Seibel
20. Surely You're Joking, Mr. Feynman! by Richard Feynman
21. Effective Java 2nd edition by Joshua Bloch
22. Patterns of Enterprise Application Architecture by Martin Fowler
23. The Little Schemer by Matthias Felleisen and Daniel P. Friedman
24. The Seasoned Schemer by Matthias Felleisen and Daniel P. Friedman
25. Why's (Poignant) Guide to Ruby by why the lucky stiff (free PDF)
26. The Inmates Are Running The Asylum: Why High Tech Products Drive Us Crazy and How to Restore the Sanity by Alan Cooper
27. The Art of Unix Programming by Eric S. Raymond
28. Test-Driven Development: By Example by Kent Beck (free PDF)
29. Practices of an Agile Developer by Venkat Subramaniam and Andy Hunt
30. Don't Make Me Think by Steve Krug
31. Agile Software Development, Principles, Patterns, and Practices by Robert C. Martin
32. Domain Driven Designs by Eric Evans
33. The Design of Everyday Things by Donald Norman
34. Modern C++ Design by Andrei Alexandrescu
35. Best Software Writing I by Joel Spolsky
36. The Practice of Programming by Kernighan and Pike
37. Pragmatic Thinking and Learning: Refactor Your Wetware by Andy Hunt
38. Software Estimation: Demystifying the Black Art by Steve McConnel
39. The Passionate Programmer by Chad Fowler
40. Hackers: Heroes of the Computer Revolution by Steven Levy (free ebook)
41. Algorithms + Data Structures = Programs by Niklaus Wirth (free PDF)
42. Writing Solid Code by Steve Maguire
43. JavaScript - The Good Parts by Douglas Crockford
44. Getting Real by 37 Signals (free PDF)
45. Foundations of Programming by Karl Seguin (free PDF)
46. Computer Graphics: Principles and Practice in C (2nd Edition) by Foley, Dam, Feiner, Hughes
47. Thinking in Java by Bruce Eckel
48. The Elements of Computing Systems by Noam Nisan and Shimon Schocken(free ebook)
49. Refactoring to Patterns by Joshua Kerievsky
50. Modern Operating Systems by Andrew S. Tanenbaum
51. The Annotated Turing by Charles Petzold
52. Things That Make Us Smart by Donald Norman
53. The Timeless Way of Building by Christopher Alexander
54. The Deadline: A Novel About Project Management by Tom DeMarco
55. The C++ Programming Language (3rd edition) by Stroustrup
56. Computer Systems - A Programmer's Perspective by Bryant and O'Hallaron
57. Agile Principles, Patterns, and Practices in C# by Robert C. Martin
58. Growing Object-Oriented Software, Guided by Tests by Steve Freeman and Nat Pryce
59. Framework Design Guidelines by Brad Abrams
60. Object Thinking by Dr. David West
61. Advanced Programming in the UNIX Environment by W. Richard Stevens
62. Hackers and Painters: Big Ideas from the Computer Age by Paul Graham
63. The Soul of a New Machine by Tracy Kidder
64. CLR via C# by Jeffrey Richter
65. Design Patterns in C# by Steve Metsker
66. Zen and the Art of Motorcycle Maintenance by Robert M. Pirsig
67. About Face - The Essentials of Interaction Design by Alan Cooper
68. Here Comes Everybody: The Power of Organizing Without Organizations by Clay Shirky
69. The Tao of Programming by Geoffrey James (free ebook)
70. Computational Beauty of Nature by Gary William Flake
71. Philip and Alex's Guide to Web Publishing (free ebook)
72. Object-Oriented Analysis and Design with Applications by Grady Booch
73. Computability by N. J. Cutland
74. Masterminds of Programming by Federico Biancuzzi
75. The Tao Te Ching by Lao-tzu
76. The Productive Programmer by Neil Ford
77. The Art of Deception by Kevin Mitnick
78. The Career Programmer: Guerilla Tactics for an Imperfect World by Christopher Duncan
79. Paradigms of Artificial Intelligence Programming: Case studies in Common Lisp by Peter Norvig (free ebook)
80. Masters of Doom by David Kushner
81. Pragmatic Unit Testing in C# with NUnit by Andy Hunt and Dave Thomas
82. How To Solve It by George Polya (free PDF)
83. Smalltalk-80: The Language and its Implementation by Adele Goldberg
84. Writing Secure Code (2nd Edition) by Michael Howard
85. Introduction to Functional Programming by Richard Bird
86. No Bugs! by David Thielen
87. JUnit in Action by Petar Tahchiev

What is the single most influential book every programmer should read?

If you could go back in time and tell yourself to read a specific book at the beginning of your career as a developer, which book would it be?

I expect this list to be varied and to cover a wide range of things.