This is a selective guide to sources of international, macro-level economic statistics. Historical data in electronic format prior to 1950 is rare. Seek the assistance of a librarian when trying to get a complete picture of what is available. Most governmental links provide current data only. Separate detailed guides are available for Finance, Health, Environment, and Sports statistics as well as micro-level data.
The basic question to ask when looking for economic data is "Who cares about what I am studying?" Unfortunately, the answer will often be no one. Ideally, look for an organization that is concerned with your research as part of its mission. Examples include the International Labor Organization focusing on labor research; the International Monetary Fund focusing on monetary and fiscal concerns; the World Bank focusing on development. What exists for one country may not exist for another country. Data is generally inconsistent across borders. Always look at the methodology.
With the exception of some governmental data, very little data is available for free. Resources for Economists on the Internet and the Princeton University Library Economics Homepage provide good starting points for what is available.