I haven't had anyone from Central or South America ask me to do their research so I'm not experienced in the specifics by country, but I do know that many families who are from Mexico or other "Latin" countries have ancestry in Spain. Spain was in the Americas while colonies on the eastern seaboard of Colonial America struggled. Like, Italy or France, Roman Catholic archives are also useful to any family history or genealogy quest in Spain. Like some other countries, the actual physical archives are in various departments/places but there is a more unifying porthole. The main branches of the National Archives of Spain include the General Archive of the Indies in Seville, the National Historical Archives in Madrid, the General Administrative Archives in Alcala de Henares, and the General Archive of Simancas.
Excerpt:
Portal de Archivos Españoles (PARES) is a documentary archive established and hosted by the Spanish Ministry of Education. It offers free access to digitized images of the Spanish Archives.
Here's where you go to find digitalized images from the archives: PARES CULTURA GOB SPAIN : DIGITAL NATIONAL ARCHIVES
At another time I'll get to posting archives in Central and South America, but for now, let's continue to focus of Europe.