Which world war?

Well, I can write about Brazil, if it helps. They got involved in WWI quite late. At first, they had a neutral stance, the same position the US and all other South American nations had. After the Germans torpedoed Brazilian vessels in 1917, protests swept the country, and Brazil eventually declared war on Germany. A medical mission was sent to the Western Front in autumn 1918, and helped to deal with the Spanish flu. There were plans for some military involvement, but the war was over before any serious action could be taken. Some Brazilian officers were in French divisions for a couple of months, but that was about it.

In 1930, Getúlio Vargas rose to power and we was in dictatorial power until 1945. During WWII he kept the country in a neutral stance until pressure from the US was too strong, and Brazil declared war on Germany in August 1942. After that, the Brazilian Navy helped patrol the Atlantic Ocean against German U-Boats, sinking several submarines off the Brazilian coast. In 1944-5, Brazil sent military forces to help in the invasion of Italy: the Brazilian Expeditionary Force (FEB, infantry) and a couple of Air Force squadrons were under command of the Americans until the end of the war.

As far as I know, Brazil was the only South American nation that effectively got involved in both conflicts. However, in 1939 there was the Battle of River Plate, when a damaged German cruiser was heavily damaged by British ships (after sinking several Allied ships in the Atlantic) and was forced to take shelter in neutral Montevideo (Uruguay). The German captain decided to scuttle the ship to avoid useless deaths, and committed suicide. The crew spread out, some stayed in South America and others eventually made their way back to Germany.

There is also evidence that some Nazi leaders fled to South America after the German defeat, specially to Argentina. The most famous case is of Adolf Eichmann, SS commander and accused of many crimes during the Holocaust, who was kidnapped by Mossad agents in the 60s and taken to Israel for trial.