1

Introduction to Algorithms 2nd edition [CLRS 2001]
Introduction to Algorithms 1st edition [CLR 1990]
by: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein.

I have both version of the book now :) and have read most of the chapters (~ 70%). This book is a-must-have (and read) to be a good programmer.

2

The Algorithm Design Manual [ADM]
by Steven S. Skiena (website).

I already have this book, a very good book.
Also a-must-have for every good programmer.

3

Programming Challenges [PC]
by Steven S. Skiena and Miguel Revilla

I also have this book. Really interesting book.
Get one copy for yourself :)

4

Introduction to the Design and Analysis of Algorithms [DAA]
by Anany Levitin

A book in design and analysis of algorithms. Have a new algorithm classification technique and use a lot of puzzles to explain concepts. Try it :).

5

Programming Pearls [PP]
by Jon Bentley

A nice programming book :), actually this book is a compilation from Bentley's writings in Communications of ACM (CACM) Newsletter.

6

The Art of Computer Programming, Volumes 1-3 [ACP]
by Donald E. Knuth

Hard to understand for beginner but worth to read (quite mathematical)
Note: I don't have this book...

7

Others

Anything else related to programming. I have a long list actually, but the first few books above are already sufficient (even though most are expensive)...