Statistical office of the European Union
The EU's statistical office, publisher of euro-area inflation, unemployment, GDP and the Economic Sentiment Indicator.
Eurostat compiles statistics for the European Union and the euro area from the national statistical institutes. Its JSON API is keyless and its data is CC BY 4.0.
Four euro-area series here come from Eurostat: core HICP, the unemployment rate, quarterly GDP, and the European Commission's Economic Sentiment Indicator, which Eurostat redistributes.