Probably it can be viewed as a variant on already posted answers (cryptography etc.), but the study of permutation groups and its application in cracking the Enigma code literally changed history (namely, the outcome of World War II). Here is an article by Marian Rejewski, one of the people involved in the code-cracking, explaining what was done and how:
http://www.impan.pl/Great/Rejewski/article.html
Rejewski and his achievements were also mentioned in answers to the following MO questions:
http://mathoverflow.net/questions/2556/real-world-applications-of-mathematics-by-arxiv-subject-area
http://mathoverflow.net/questions/36094/notable-mathematics-during-world-war-ii
