The following agencies and sites are excellent resources for basic statistical data sets about Latin America & the Caribbean. Please also see the research guide covering statistics.
CEPALSTAT (United Nations Economic Commission for Latin America & the Caribbean)
Inter-American Development Bank
Pan American Health Organization
UNdata (United Nations)
Association of Religion Data Archives
Centro Centroamericano de Población
ICPSR (Inter-University Consortium for Political and Social Research)
Latin American Electronic Data Archive
Latin American Migration Project (Princeton)
Latin American Mortality Database (U. of Wisconsin)
Latin American Public Opinion Project (Vanderbilt)
Montevideo-Oxford Latin American Economic History Database (MOxLAD)
The Library subscribes to Data Planet, a dynamic statistical repository. It includes growing numbers of relevant data sets on a single platform with various visualization and analysis capabilities, and is fairly easy to cite. I recommend exploring the various data available for Latin America by country through the appropriate DataPlanet LibGuides.