Our World in Data provides a wide range on general socio-economic data.
World Economic Outlook Database - IMF Data on key macroeconomic aggregates, including projections, for many countries. Advantages: consistency, projections. Check for latest [biannual] update (this link leads to the April 2015 version).
World Development Indicators - World Bank data on many macroeconomic and development indicators. Key advantage: wide coverage (concerning variables, over time and across countries).
FRED - a great tool for macroeconomic and financial data by the Federal Reserve Bank of St. Louis. Focuses on industrialized countries (but not exclusively) and handles data management quite easily.
Penn World Tables - key data set for real sector/national accounts macro data (especially GDP, growth etc.). Key advantage: historical availability and comparison of price levels (PPPs) across countries to compare living standards.
OECD Stats - extremely wide and interesting set of economic indicators, unfortunately mostly limited to OECD countries. Especially check out the STAN Structural Analysis database for industry level data.
EU ameco - provides annual macroeconomic data on the EU-28 (and other OECD) countries (the data come in txt format).
The Groningen GGDC 10-Sector Database provides data on value added and employment by sector for several countries dating back as far as 1950.
Other IMF Data - includes many macroeconmic and financial datasets, including international financial statistics (IFS), balance of payment data (BOPS), direction of trade statistics (DOTS), commodity prices etc. Furthermore, IMF offers an archive of daily exchange rates.
Data on financial development and structure is available from the World Bank.
Data on banking and other financial crises are available from Laeven and Valencia (1970-2011, with update until 2017 here) and Reinhart and Rogoff (1800-2010).
Bank Ownership Around the World by Ugo Panizza shows ownership shares (foreign and state) at the country-year level in 181 countries over 1995-2020.
Data on tax havens and their impact are available from the EU Tax Observatory and https://missingprofits.world/
The Heritage Foundation collects data on different aspects of economic freedom (annual data starting in 1995). Another dataset on economic freedom (dating back to 1970 in 5 year intervals, annual from 2000) is provided by the Fraser Institute.
Further data on institutions, as well as conflict, violence, and war is available for a long time period from the Center for Systemic Peace. and the Uppsala Conflict Data Program.
The Joint External Debt Hub (JEDH) offers external debt data and selected foreign assets (on a quarterly basis).
Oxford Economics offers some interesting data bases, especially macro data on monthly/quarterly basis. Subscription is required but you may do well with a trial version when for example working on a seminar paper or thesis.
The Wittgenstein Centre offers data (since 1970) and projections (until 2100) on population, demographics, and human capital/education.
UNCTAD Statistics - trade and FDI data, covers some aspects that other key macro databases do not.
WITS - World Integrated Trade Solution database. Key advantage: breakdown of trade data (trading partners, product groups etc.).
CEPII offers a lot of great trade and macro data (including data on geographical distance and legal heritage, used in several trade models). While most of it is free, you will still have to register.
The USITC Gravity Portal offers data and computer code related to gravity modeling of international trade.
The World Bank's Exporter Dynamics Database covers basic micro-characteristics of the export sector (number of exporters, their size, and their growth), the degree of concentration and of diversification of exporters, their dynamics in terms of entry, exit, and survival, and the average unit prices of the products they trade for 70 countries over the period 1990/2005-2012/2014 (depending on the sample).
OECD's Structural and Demographic Business Statistics (SDBS) offers sectoral data on the industrial structure of OECD economies.
The World Bank's Labor Content of Exports Database is a great data source about labor's value added in exports, allowing for cross-sector ("input-output") linkages and wide coverage (up to 120 countries since 1995).
The OECD provides its analytical AMNE database on multinational firms and global value chains.
The WIOD provides a World Input-Output database since 1995 (but unfortunately only covers a limited number of 40 countries). Furthermore, it includes indicators and material about Global Value Chains. OECD's TiVA database also covers several indicators of GVCs and trade in value added. GVC indictors are further available from the UIBE.
The Design of Trade Agreements (DESTA) database contains information on 790 preferential trade agreements between 1947 and 2019 (with information on issues such as sector coverage, depth of commitments, trade integration and compliance tools).
PovcalNet provides data and tools for poverty analysis
The World Bank also provides a Poverty & Equity data collection, see also the related links and data resources linked there. Furthermore, it offers the LSMS data catalogue on household surveys and micro data.
UNU-WIDER's World Income Inequality Database (WIID) is probably the most comprehensive income inequality database. An alternative is Frederick Solt's Standardized World Income Inequality Database (SWIID) or the World Inequality Database.
Several of the most important poverty and inequality measures are also included in WDI.
The WB Poverty Analysis Toolkit provides a battery of very useful STATA programs for advanced poverty and inequality analysis.
The GC Wealth Project provides data on wealth, wealth inequalities, and wealth transfers and related tax policies, across countries and over time.
National data on temperature and precipitation including predictions into the future are nicely prepared by the World Bank Climate Change Knowledge Portal (CCKP).
Natural disaster data is provided by EM-DAT. Those data are also available via Our World in Data.
The World carbon pricing database (WCPD) has sectoral coverage and prices associated with carbon pricing mechanisms implemented worldwide at the national and subnational levels since 1990.
The University of East Anglia provides a wide range of climate data, also with detailed geographical locations. Large-scale drought and flood events between 1950 and 2016 on a granular geographic level are also available from the Global Drought and Flood Catalogue (GDFC).
A rich dataset on weather events and economic growth (on the national and sub-national level for 214 countries) for the period 1950-2015 is available from the study of Acevedo et al. (2020).
wbopendata provides a STATA tool to access World Bank data.
You can search and find economic articles with data for replication here: https://ejd.econ.mathematik.uni-ulm.de/
DataViva and DataUSA present a rich body and nice visualization of very diverse data for Brazil and the USA, respectively that might be useful for country case studies.
Global dataset of pandemic and epidemic-prone disease outbreaks.
Google offers a specialized Dataset Search.