Cryptography was used extensively during World War II, with a plethora of code and cipher systems fielded by the nations involved. In addition, the theoretical and practical aspects of cryptanalysis, or codebreaking, was much advanced.
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Probably the most important codebreaking event of the war was the successful decryption by the Allies of the German "Enigma" Cipher. The first complete break into Enigma was accomplished by Poland around 1932; the techniques and insights used were passed to the French and British Allies just before the outbreak of the War in 1939. They were substantially improved by British efforts at the Bletchley Park research station during the War. Decryption of the Enigma Cipher allowed the Allies to read important parts of German radio traffic on important networks and was an invaluable source of military intelligence throughout the War. Intelligence from this source (and other high level sources, including the Fish ciphers) was eventually called Ultra.
A similar break into an important Japanese cipher (PURPLE) by the US Army Signals Intelligence Service started before the US entered the War. Product from this source was called MAGIC. It was the highest security Japanese diplomatic cipher.
Australia
France
Germany
Italy
Japan
Poland
Soviet Union
As is common with World War II discussions of cryptology, there is a curious absence of information on Soviet efforts and accomplishments. Given the Red Army offenses on the Eastern Front, they must have obtained Enigma machines. What they did with them seems to be an unanswered question.