Iberia is probably the most frequently used airline for cheap flights to South America. Airfares are generally excellent value, and the airline serves multiple destinations throughout Central and South America. For open jaw flights to South America, it is often the best option (open jaw flights are into one city, and out of another). The business class product is excellent with flat beds and good service. Sadly, Iberia has a (deserved) reputation for rude staff, flight delays and lost baggage. Having said that, they are often have the cheapest flights. There are flights to Central American destinations such as Mexico City, Cancun, Guatamala City, Managua, San Jose and Panama City. In South America, Iberia flies to Caracas, Bogota, Quito, Guayaquil, Lima, Bolivia (via Sao Paulo), Rio de Janerio, Buenos Aires and Santiago.
Frequent flyers to South America should definately join Iberia's frequent flyer programme - Iberia is one of the airlines most likely to offer free business class upgrades to it's frequent fliers.