Eurostat: the European Union's centralized statistical agency. View preconfigured tables, maps and graphs; download publications, posters and geographic data.
Eurostat produces data for EU policy development in regional development, economic union, agriculture and many other areas, and promotes harmonization of member state statistics. See also Statistics Explained: Your guide to European [i.e. EU] statistics.
Important: About Eurostat data harmonization, with timeline.
What are Europe's non-EU countries?
Iceland, Norway and Switzerland are the largest non-EU members. Others: Albania, Bosnia and Herzegovina, Croatia, Liechtenstein, Macedonia, Serbia and Turkey.
And now, Great Britain.
European indicators (from Statistics Austria)
Descriptions/explanations of EU's European structural indicators, Principal European Economic Indicators (PEEIs), sustainability indicators, and Euro-indicators. This site includes links to sources for harmonized data.
European Statistical System
The European Statistical System works with Eurostat and with member states' statistical agencies with the aim of working toward comparable statistics at EU level. There is also coordination with candidate member countries and with external data sources such as OECD, the UN, the International Monetary Fund, and the World Bank.
International and Supranational Bodies (selected)
Data centers and research centers, such as the WZB Berlin Social Science Center, maintain catalogs or lists of data sources. The WZB's list is here: https://wzb.eu/en/literature-data/search-find/data-sources.