This blog offers a handful of useful websites with commonly used datasets for general research.

Data and statistics: Open Data Sets by topic

• Datasets with the following topics: Agriculture; Chemistry Data & Spectra; Criminal Justice; Demographic-Social; Economic & Financial; Education; Elections & Voting (International); Elections & Voting (U.S.); Energy; Environment; Geographic Information Systems (GIS)/Geotechnology; Geosciences; Health; Labor; Polling Data (US & International); Social Media Data & Stats; Sports; Transportation; Other specialized data sets

Eurostat

• Datasets about anything and everything European

NCU Research process

• Searching datasets made easy

OECD.stat

• Data and metadata for OECD member states and selected non-member states

Pick10chart

• Datasets with the following subjects: Business and Employment; Crime/Conflict/Drugs; Internet; Finance; Health; Entertainment; Government; Transportation; Weather & Environment; Miscellaneous

R-dir

• Some really good starting places for further exploration of the free data set you want

Statistical Data Sets

• Many, many interesting links with emphasis on mathematical research

World Bank Open Data

• Arguably the most commonly used datasets in the world