Amt (Ämter): Translate as authority (authorities). This is a grouping of Gemeinden at a lower level than a Kreis. (see Amt (country subdivision))
Bezirk: As part of a town or city, translate as borough; as an abbreviation of Regierungsbezirk, see below. In references to former East Germany, do not translate, as the term does not equate to any unit in West Germany, let alone other European countries.
Bundesland (Bundesländer): See Land, Länder below. Note however that Bundesland/länder in Austria are translated as province(s).
Gemeinde: Translate as municipality.
Gemeindeverband: Translate as municipal association.
Kreis: Translate as district.
Kreisfreie Stadt: As this is exactly the same level as a Stadtkreis, the translation urban district will generally be satisfactory. Should it be necessary to distinguish between this term and a Stadtkreis, use town constituting a district in its own right.
(Bundes-)Land, (Bundes-)Länder: Translate as federal state(s), adding "German" if necessary for clarity, or, alternatively, leave the terms in German.
Landkreis: Translate as rural district.
Regierungsbezirk/Bezirksregierung: If you translate these terms, use government region/regional government, not government district/district government, so as not to cause confusion with Kreis.