I tried to build a list with links to useful free and open geodata sources. Are you missing any important services? Please tell us in the comment section.
ALOS/PALSAR Data: Global 25m resolutions PALSAR-2/PALSAR mosaic and forest/non-forest map
ALOS World 3D – 30m: Global digital surface model (DSM) dataset with a horizontal resolution of approx. 30-meter mesh (1 arcsec)
CHELSA Climate: Free climate data at high resolution
Copernicus Land Monitoring Service: various bio-geophysical products of global land service (related to the themes vegetation, energy, water, cryosphere and hot spots), pan-european data sets (e.g. land cover, optical VHR2 data, settlement maps) and local data sets (e.g. Natura 2000)
Diva-GIS data sets: Country level data for any country in the world: administrative boundaries, roads, railroads, altitude, land cover, population density; global climate data
EarthEnv: Global, remote-sensing supported environmental layers for assessing status and trends in biodiversity, ecosystems, and climate
European Soil Data Center: various soil data and related/derived information (registration via e-mail is requested)
ETOPO1 Global Relief Model Download: 1 arc-minute global relief model of Earth’s surface that integrates land topography and ocean bathymetry
Geofabrik OpenStreetMap Data Extracts: data extracts (worldwide) from the OpenStreetMap project which are updated every day
Global Forest Watch Datasets: Massive datasets of global tree cover, tree cover loss/gain, forest types, land cover, concessions, protected areas, forest fires, and much more
Harmonized Landsat and Sentinel-2: Harmonized Surface Reflectance Product from Nasa
Jonathan de Ferrantis Digital Elevation Data: “Perhaps I am biased, but I still believe that for many areas, the best available data are still on this site!” (Jonathan de Ferrantis)
Nasa EarthData Search: Search, discover, visualize, refine, and access NASA Earth Observation data
The Humanitarian Data Exchange: Official Data from the United Nations Office for the Coordination of Humanitarian Affairs (OCHA), first starting point when you search for vector data like boundaries etc.
Theia – Land Data Center: Theia (French national inter-agency organization) is offering scientific communities and public policy actors a broad range of (satellite) images at different scales, methods and services.
USGS Earth Explorer: Archive of the U.S. Geological Survey, query and order satellite images (e.g. Landsat), aerial photographs, and cartographic products and much more
USGS GloVis: Search and order tool for selected satellite data from the U.S. Geological Survey