In the course of WWII both the Allies and the Axis powers were able to gain information of great value from reading their enemies secret communications. In Britain the codebreakers of Bletchley Park solved several enemy systems with the most important ones being the German Enigma and Tunny cipher machines and the Italian C-38m. Codebreaking played a role in the Battle of the Atlantic, the North Africa Campaign and the Normandy invasion.
In the United States the Army and Navy codebreakers solved many Japanese cryptosystems and used this advantage in battle. The great victory at Midway would probably not have been possible if the Americans had not solved the Japanese Navy’s JN25 code.
On the other side of the hill the codebreakers of Germany, Japan, Italy and Finland also solved many important enemy cryptosystems both military and diplomatic. The German codebreakers could eavesdrop on the radio-telephone conversations of Franklin Roosevelt and Winston Churchill, they could decode the messages of the British and US Navies during their convoy operations in the Atlantic and together with the Japanese and Finns they could solve State Department messages (both low and high level) from embassies around the world.
Britain, the Soviet Union and the United States did not have impenetrable codes. In the course of WWII all three suffered setbacks from their compromised communications. One of the worst failures of US crypto security was the extensive compromise of State Department communications in the period 1940-44.