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Macrodata (national accounts, sectoral data, monetary and financial statistics, international trade, government accounts)
Eurostat (macroeconomic, sectoral, and government data)
https://ec.europa.eu/eurostat/data/database
European Commission: AMECO
https://ec.europa.eu/economy_finance/ameco/user/serie/SelectSerie.cfm
European Commission: quarterly economic forecasts
Bank for International Settlements (financial and banking data)
https://www.bis.org/statistics/index.htm?m=6%7C37
OECD (macroeconomic, sectoral data)
ECB (monetary, financial, and macroeconomic data)
IMF (financial and macroeconomic data)
http://data.imf.org/?sk=388DFA60-1D26-4ADE-B505-A05A558D9A42
IMF (international trade data)
https://data.imf.org/?sk=9D6028D4-F14A-464C-A2F2-59B2CD424B85
World Bank (development and macroeconomic data)
UN Intergovernmental Panel on Climate Change
Microdata (data on individual households, workers, companies, students, etc.)
European Union (labour force data)
https://ec.europa.eu/eurostat/web/microdata/european-union-labour-force-survey
European Union (SILC)
European Union (earnings data)
https://ec.europa.eu/eurostat/web/microdata/structure-of-earnings-survey
European Investment Bank (survey on investments)
https://www.eib.org/en/about/economic-research/surveys-data/investment-survey.htm
World Bank
https://microdata.worldbank.org/index.php/catalog
In addition to data provided by international organizations, there are plenty of national data sources provided by national governments, national statistical offices, national central banks, etc.).
Here are a number of important data sources from national central banks:
Bundesbank
https://www.bundesbank.de/en/statistics
Bank of England
https://www.bankofengland.co.uk/statistics
US Federal Reserve
https://www.federalreserve.gov/data.htm
Banque de France
https://www.banque-france.fr/en
Banca d’Italia