Recommended Reading

There are many excellent references online, and also many books which are worth purchasing or locating in a local library. 

Online Resources

• CipherClerk Online Tool 

• Army Field Manual on Basic Cryptanalysis 

• Introduction to Cryptography - From Network Associates' PGP Documentation

• Lanaki's Classic Cryptography Course 

• Cryptography Overview - NIST 

• Cryptography A - Z

• Cryptologia Cryptography Journal

• Crypto-Gram - Bruce Schneier publishes a monthly online newsletter on modern cryptography. If I'm looking for analysis or debunking of a current system, his site is the first place I check.

And of course, lots of other great info can be found here: http://www.google.com

Books

The Code Book by Simon Singh - If you're completely new to cryptography, this is an excellent starter book. It gives a good overview of cryptography from ancient times until today, and is an interesting read.

Elementary Cryptanalysis - Helen Fouché Gaines - Written in 1939, this book (also published under the title Cryptanalysis - a study of ciphers and their solutions) is considered one of the classics.  No cryptanalytic library should be without it.

The Codebreakers - David Kahn - A well-researched tome written by one of the editors of the Cryptologia journal.

Applied Cryptography - Bruce Schneier is one of the most famous names in modern cryptography.  He also publishes a (free) monthly electronic newsletter called Crypto-Gram which is well worth subscribing to.

Practical Cryptography - Niels Ferguson & Bruce Schneier

Military Cryptanalysis, Part I, Monoalphabetic Substitution Systems - William F. Friedman is arguably one of the most famous cryptanalysts in history.

Military Cryptanalysis: Transposition and Fractionating Systems (Cryptographic Series , No 61, Part 4) - Friedman

Cryptography: Theory and Practice - Stinson

Cryptography Demystified - John E. Hershey

Cryptological Mathematics - Robert Edward Lewand

Modern Cryptography: Theory and Practice - Wenbo Mao

Elementary Cryptanalysis: A Mathematical Approach - Abraham Sinkov

Introduction to Cryptography - Johannes A. Buchmann

Cryptography : The Science of Secret Writing - Laurence D. Smith

Cryptanalysis of Number Theoretic Ciphers - Wagstaff

Cryptanalysis of the Double Transposition Cipher: Includes Problems and Computer Programs - Wayne G. Barker

Cryptanalysis of the Shift Register Generated Stream Cipher Systems (C-39) - Barker

Statistical Methods in Cryptanalysis - Kullback

Enigma - Robert Harris

Encyclopedia of Cryptology - David E. Newton

Handbook of Applied Cryptography - Menezes, Oorschot, Vanstone - If you're interested in the hardcore math of the modern algorithms, this is one of the top-recommended books around for current high-tech crypto systems. Chapters are also available for free download here.

(2/20/2006) Though I do not put my own book in the same class as the above titles, I feel that it would be an inappropriate omission if I did not at least mention it here:
The Mammoth Book of Secret Code Puzzles - Elonka Dunin, 2006 - A collection of several hundred cryptographic puzzles, along with basic explanations of several cryptographic techniques, and solving tips.