Currency war was one of the effects of the Great Depression. In order to protect their own economies from foreign competition and make their products more competitive in the international markets, many governments increased tariffs, abandoned the gold standard (the correspondence with the gold reserves they had and the circulating money in their countries) and devalued their currencies. The governments tried to save their economies to the detriment of the other countries. This policy was known as "beggar thy neighbour" (impoverish your neighbour). The main fighters in this war were the former allies in WW1: the USA, France and the United Kingdom. The government of the UK decided to take the sterling pound out off the gold standard in September 1931, because their gold reserves had reduced and they decided to suspend the exchange of pounds for gold. Other countries like the Scandinavian ones and Japan did the same in 1931. The USA left the gold standard in 1933 and France and Belgium stayed on the gold standard until 1935. The studies about the Great Depression confirm that the economies of the countries which left the gold standard first recovered earlier and the depression was longer in the countries which left standard later. The 30s currency war ended with the signature of the Tripartite Agreement in 1936.
In the current crisis there is also a non declared currency war between different countries. The US dollar and the Japanese yen have been devalued several times since 2009 and the Chinese yuan has appreciated a little bit under the USA pressure. It seems that the euro is losing the war up to now. Here you have more information about this war:
This chart summarizes the basic information about what a currency war is and its consequences:
And here you have some more cartoons about the current currency war: