In South America, KLM flies via Amsterdam to Mexico City, Lima, Quito, Guayaquil, and Sao Paulo. There are connecting flights to various destinations in Brazil, and one can also connect from Sao Paulo onwards to Buenos Aires.
Air France has flights to South American countries including Mexico City, Caracas, Bogota, Sao Paulo, Rio de Janiero, Buenos Aires and Santiago. Via Caracas or Bogota, one can also catch a connecting flight onwards to Quito, Guayaquil and Lima.
Both KLM and Air France have very cheap flights from Europe to Central America. Such flights will also involve a change of plane in Miami, Houston or Atlanta. There are cheap flights to Central America cities such as Guatemala City, Managua, Tegucigalpa, Panama City and San Jose.