Essential library

These are books that most computer programmers should have. If you need to know about the topic, you can buy the book sight unseen, and know that you will not be disappointed.

Essential

The C Programming Language, 2nd Ed.

Unix Network Programming, 2nd ed. (rec. by elim)

Salas and Hille's Calculus (rec. by elim)

Algorithms in C (rec. by elim)

Abelson and Sussman: Structure and Interpretation of Computer Programs

Foley, van Dam, Feiner, and Hughes

Stevens: Advanced Programming in the Unix Environment (rec. by josh)

Camel book

Hennessy and Patterson: Computer Architecture, a Quantitative Approach

Tufte: The Visual Display of Quantitative Information

Writing Solid Code

Feynman Lectures

Bruce Schneier: Applied Cryptography, 2nd ed.

Valuable

These are good books. If you really want to know the subject in detail, go and get them.

Advanced Perl Programming

Java in a Nutshell, 1.1 ed (already obsolete, sadly)

Deep C Secrets (rec. by yosh)

Unicode

What's your experience? Do you have a favorite essential book? Send me a cite and a brief review of why the book merits listing here.