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barrkel comments on The Best Textbooks on Every Subject - Less Wrong
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General programming: Structure and Interpretation of Computer Programs. Focuses on the essence of the subject with such clarity that a novice can understand the first chapter, yet an expert will have learned something by the last chapter.
Specific programming languages: The C Programming Language, The C++ Programming Language, CLR via C#. Informative to a degree that rarely coexists with such clarity and readability.
AI: Artificial Intelligence: a Modern Approach. Perhaps the rarest virtue of this work is that not only does it give about as comprehensive a survey of the field as will fit in a single book, but casts a cool eye on the limitations as well as strengths of each technique discussed.
Compiler design: Compilers: Principles, Techniques and Tools. The standard textbook for good reason.
I don't agree on the dragon book (Compilers: Principles, Techniques and Tools). It focuses too much on theory of parsing for front end stuff, and doesn't really have enough space to give a good treatment on the back end. It's a book I'd recommend if you were writing another compiler-compiler like yacc.
I'd rather suggest Modern Compiler Implementation in ML; even though there are C and Java versions too, a functional language with pattern matching makes writing a compiler a much more pleasant experience.
(I work on a commercial compiler for a living.)
+1 for ML (and purely functional languages) used for implementing compilers.