Berlin's boroughs ("Bezirke") as KML and GeoJSON
The Statistical Office of Berlin and Brandenburg provides kml shapefiles of a number of administrative areas in Berlin, such as the localities within each borough. As I could not find the borders of the boroughs themselves, I merged all the the localities, thus providing only the 12 boroughs.
The source of the shapefiles can be found at https://www.statistik-berlin-brandenburg.de/produkte/opendata/geometrienOD.asp?Kat=6301
The data is provided on a CC-BY basis: http://creativecommons.org/licenses/by/3.0/de/