Eurostat is the statistical office of the European Union. It offers economic, demographic, and social data, mostly for the members states of the EU, but in some cases also for other countries. Geographical data (GIS) is also available. Eurostat tries to ensure that the data are comparable over time and countries. You can browse the statistics by theme, or use the bulk-download facility to download larger amounts of data.
Eurostat publishes technical guidelines and manuals. These are useful if you need to know precisely how certain data are defined (or if you suffer from insomnia). There are no published guidelines for the use of the website, but finding data is relatively straighforward.
The OECD publishes statistics for OECD countries and selected non-member countries. Topics include demographics, health, education, and finance.
The OECD presents its data on different websites. The most important ones are OECD Data and OECD Stats. OECD Data presents data in an accessible way, including graphs that can be edited and exported. The OECD Stats website features more options for bulk downloads of raw data series.
You can consult the User guides for OECD Stats here.
The World Bank publishes a large number of data series for countries around the world, with a focus on development.
The World Bank's Open Data site gives easy access to data for countries, topics or indicators, and allows you to download data at the click of a button. The DataBank has functionality to perform customised queries and selections, and to create data visualisations. Not all data series that are available in the DataBank can also be found on the Open Data site.
The third-party applications listed here make use of (access to) Worldbank data. For example, there are applications that let you import worldbank data series directly into Stata, Excel, or R.
The international Monetary Fund publishes a large number of financial and economic data series for countries around the world. Data can be downloaded in bulk. You can also visualize data on the website, and export the resulting graphs for use in your paper.
You can find a list of Help documents here.