For macroeconomics the standard sources are here: the Penn World Table, the Maddison Project Database and the World Input-Output Database from the Groningen Growth and Development Centre, the EU KLEMS, Asia KLEMS and World KLEMS productivity accounts, BIS financial statistics and UN Comtrade trade data. DBnomics gathers series from INSEE, Eurostat, the IMF and others behind one API, and the Atlas of Economic Complexity and the Observatory of Economic Complexity cover trade structure.
The list also holds many narrow, frequently updated sets: job postings, wages by occupation, tariff schedules, rent and housing prices, cloud GPU and VPS prices, and consumer price trackers for single products. These are mostly CC BY and published by small companies, so check how prices are collected and whether the series is a snapshot or a maintained index.
For cross-country work, confirm whether figures are nominal or real, which base year and currency are used, and whether values are adjusted for purchasing power. Revisions are common, so record the version you used, for example Penn World Table 10.0 rather than just the project name. A few older links, such as Jon Haveman's international trade data, now point to Wayback Machine captures.