Can anyone give me a hint where to find a list of the geographical centers of all countries over the world? (In case I don't want to calculate them from other data.)
I found several sources of "country centroids."
Country Centroids, from worldmap.harvard.edu, available to download in many formats (Zipped Shapefile, GML 2.0, GML 3.1.1, CSV, Excel, GeoJSON, GeoTIFF, JPEG, PDF, PNG, KML, View in Google Earth). Also available as a web map service. This dataset comes with a lot (80-ish) of attributes.
From Google, there's a simple table of lat/long coordinates for countries. Just 4 columns: 2-letter country code, latitude, longitude, and country name. (There's no download link. Just highlight the table and copy-paste it into a spreadsheet.)
On periscopedata.com, Country Centroids: Geographic centers of countries in lat-long coordinates. Posted by a site user named Sean Cook, self-described Product Analyst @ Facebook
And of course there are many sources of country boundaries, which you can convert to centroids and export as lat/long coordinates in any GIS software.