Statistical compendia are the first place to look for statistics and sources of data when you don't know who collects the data and you suspect they may be collected administratively (e.g., by a government agency) or regularly (e.g., an annual survey). Even if the compendium does not have the exact data you need, use it as a "guide to data sources" and follow the source notes to the originating agency, where you are likely to find more similar data and statistics.
Most countries have agencies responsible for collecing national statistics. These agencies usually produce compendia similar to the Statistical Abstract of the United States. A good way to begin finding data for a foreign country is to identify the national statistical agency, then look on their site for their annual statistical yearbook or report. Also useful are the yearbooks of central banks.
Like national statistical agencies, government agency and NGO and IGO web sites can be large and occasionally difficult to navigate, especially for the first time visitor. Also like statistical agencies, most government agencies and NGOs and IGOs have annual reports, yearbooks, or compendia. Look for these annual publications on the web site as a guide to available data. Below are just a few examples.