The National Aeronautics and Space Administration (NASA)'s Earth Observing System Data and Information System (EOSDIS)
The National Center for Atmospheric Research (NCAR)'s Climate Data Guide
The National Oceanic and Atmospheric Administration (NOAA)'s Climate Data Online
find more data sources in the "Additional Data Access" section on the page
The Intergovernmental Panel on Climate Change (IPCC)
US Environmental Protection Agency (EPA)
The European Space Agency (ESA) Climate Office Open Data Portal
World Resource Institute Data
Climate Watch Data Explorer
open access under the Creative Commons CC BY 4.0 license
International Opinion Poll Data Guide
Government Statistical Agencies
Country Statistical Yearbooks (some print & PDFs)
ICPSR's International Data (search country name)
ProQuest Statistical Insight (use topic & then filter)