This isn't really true, considering the fact that nearly every Latin American country became involved in the Second World War from the attack on Pearl Harbour until 1945. Most simply declared war on the Axis powers and provided supplies to Allied forces, however some countries such as Argentina provided volunteers.

At least two Latin American countries provided direct military support: Mexico provided a fighter squadron that served under the US 5th Air Force in the Pacific. Brazil (probably one of my favourite wartime histories), whose fascistic dictator Getulio Vargas had argued for strict neutrality before 1942, entered the war under popular pressure after German Uboats attacks on Brazilian shipping inflicted over 1000 casualties. Before 1942, the government's unwillingness to take part led to the circulation of a popular saying that went: "it's more likely for a snake to smoke a pipe, than for the BEF go to the front and fight." When they finally did enter the war, Brazil sent a combined air and army expeditionary force of around 25,000 men nicknamed "cobras fumantes" - smoking snakes, that saw action in the conquest of the Italian peninsula.

The political implications of involvement with the Allied war effort are arguably more interesting than their actual military achievements, at least in my opinion; many of these countries were dictatorships whose wartime measures led to popular resistance and their eventual overthrow. For example, Brazil's (again, my favourite) dictatorship under Vargas voluntarily ceded power in 1945 because a fascistic dictatorship was simply untenable after wartime anti-fascist rhetoric, direct Brazilian involvement in combat and the aftermath of the war in Europe made such a government potentially massively unpopular and a liability in post-war international politics (however that didn't stop Peron's Argentina from going balls-off-the-wall fascist from '46 until '55).

Brazil entered World War 2 as an active combatant in 1942, sending a divisional sized expeditionary force for service in the Italian campaign in 1944.

Though it is often overlooked in English language historiography, (I'm having trouble finding anything more than their location on campaign maps), many of the existing 'developing nations' as we would call them now did join the United Nations during the War. Most often this took the form of economic aid and supplies to the Western Allies, with the exception of Brazil as noted above. If you want to know more I suggest Ready, J. Lee. Forgotten Allies: The Military Contribution of the Colonies, Exiled Governments and Lesser Powers to the Allied Victory in World War II, for more information.

hi! you may be interested in a few previous posts

• Was South America involved in WWII to any significant degree?

• There is a lot of material on US and Canada involvement in European theater in WWII. However, I can't recall roles other Western hemisphere countries played. Especially large ones such as Brazil, Argentina, Chile, Mexico, etc.

• Why did so many countries in Latin America and the Middle East join WWII after the bombing of Pearl Harbor?

• Why did Brazil become involved in WWI and WWII? - Brazil

• The role of the Middle East, South America, India, and the non-Pacific parts of Asia during World War II - Mexico

• What was Mexico's role in World War II? - Mexico

Another interesting LATAM related WWII conflict was the Battle of the River Plate, where the Graf Spree cruiser was sunk. I believe this was the only naval battle south of the Ecuator in the entire conflict.

http://en.wikipedia.org/wiki/Battle_of_the_River_Plate

The wreckage from scuttling the ship was recently front-page news as a group of divers lay claim to millions of dollars worth of pieces, including a 2m Nazi eagle crest. There is much controversy on what to do with the crest due to the Nazi emblem on it.

http://en.wikipedia.org/wiki/German_cruiser_Admiral_Graf_Spee