Are there any laws that were installed by the Nazis that remain on the statutes of any non-German country that was occupied by the Nazis?
I can think of one example, sort of. When the Nazis occupied Czechoslovakia, they forced them to switch to driving on the right side of the road. After the war, they never switched back. Czech Republic and Slovakian drivers drive on the right side of the road today.
It has long since ended, but when I first visited France in 1964 you had to show your passport in order to register at a hotel and the hotellier had to inform the police of the passport (or id) number of every registrant and I was told that this was left over from the occupation. I think French still have to have id cards and I believe that is left over from the occupation and the Vichy. Id cards are effectively required in the US now, at least if you want to do ordinary things like travel.
Interestingly that (clumsily worded) OP was inspired by French ID cards - I guessed they were a legacy of Vichy, but was unsure.
So another question is: is there resentment of any of these laws as a result of their origin, rather than the laws themselves?
I haven’t a cite (yet) but I think the ideas of universal registration of citizens, the issue of identity papers and the registration of identity papers at hotels, etc, all long predate the German occupation of France.
Nor are they confined to France; similar measures apply in many European countries, including countries never occupied by the Axis.
I think that this is due to an earlier war of conquest; the Napoleonic wars, in which rationalist views of organising society, stemming from the French Revolution, were carried throughout Europe.
Prussia had identity cards from at least 1848, well before the Nazis: http://www.research.umbc.edu/~lmoren/ALMA/GEOHIS.HTM I assume this extended to the rest of Germany following unification in 1871, but I don’t know.
Belgium has had universal registration since 1856 and identity cards since 1919: http://reform.house.gov/gefmir/hearings/2001hearings/1116_nationa._id/veestraeten_testimony.doc