With respect to Germany: When Hitler assumed power, the Expressionist wave in German film-making had already come and gone. Film directors, writers, cinematographers and actors, particularly ones who had reason to be troubled by the rise of the NSDAP - Jews, immigrants, and so on - were already leaving the country. Economic uncertainty and political discomfort led many filmmakers of this era, such as Ernst Lubitsch and Fritz Lang, to emigrate to America in the period between 1920 and 1933.

Propaganda was integral to the Nazi regime, and so like many industries considered to be of strategic value, the NSDAP nationalised the film industry, seizing control of Universum Film AG (Ufa), Germany's major film studio. Dr Mabuse and Metropolis were both produced at Ufa, which illustrates how important it was. Ufa had a few different chief executives during the period leading up to the war, but it was a de facto arm of Goebbel's propaganda apparatus, though the methods of control and political pressure were various and changed during the period. I won't get into the tedious legalities of how Goebbels exerted control over the German film industry, but suffice to say that Ufa was purged of "undesirables" (Ie, jews, leftists, and other enemies of the Nazi state) and followed an agenda set by the German government propaganda system.

This should not be taken to mean that Ufa spent the years between 1933 and 1945 making nothing but Nazi propaganda films; rather, the German film industry continued to produce a diversity of films during this period, most of which were industrial, romantic entertainment cinema similar to what Hollywood was outputting at the time. However, those films were still written and produced in accordance with the national socialist worldview - so even escapist, entertainment cinema would have a role in constructing the othering images that the Nazi state used to justify its actions against "undesirables." So while I'm reluctant to classify those films as "propaganda," they were part of the (Incredibly sophisticated, for their time) nazi media strategy.

Propaganda under Goebbels took on an almost mythical status. Films like Triumph of the Will, one of the most important nazi propaganda films, were not made by jobbing directors trying to pay the bills. Leni Riefenstahl was not only a legitimately talented director, she advanced cinematic language in the process of creating images that would serve to justify and mythologise the nazi regime.

I can't say whether all this really worked to the extent it was intended to, and whether the german people's resolve to fight on was really boosted by the massive propaganda effort - That's a bit outside my scope. But I think that, between the degree of control that was exerted over the media, and the resources allocated to help people like Riefenstahl make propaganda films, the Nazi leadership certainly believed cinema to be an instrumental part of their political strategy.