You can find lists of good German reads and films below - and more!
Elizabeth and her German Garden (1898; originally in English) by Elizabeth von Arnim: This is Australian-born Mary Annette Beauchamp's highly successful, comic, semi-autobiographical take on a young woman's attempt to integrate into nineteenth-century Junker society. Beauchamp married Graf Henning August von Arnim-Schlagenthin in 1891 and her experiences inform much of her writing. Elizabeth and her German Garden and other novels by von Arnim can be downloaded from Project Gutenberg or audiobooks can be found at Librivox.
Felidae (1989) by Akif Pirinçci: Tomcat Francis has moved to a large German city with his 'can opener' (human owner). There, he investigates a series of murders committed against cats and soon finds himself following a grisly trail. A graphic novel that ponders, among other themes, political and religious extremism. Felidae was made into an animated film, directed by Michael Schaack, in 1994.
Der Räuber Hotzenplotz (1962; English: Robber Hotzenplotz) by Otfried Preußler: A classic illustrated children's story about the adventures of Kasperl and Sepperl as they set out to rescue their grandmother's coffee mill, stolen by Robber Hotzenplotz. The story was made into a film in 1974 and can be viewed online here. Many of Preußler's books have been translated into English.
Films & TV
Das merkwürdige Kätzchen (2013; in English as The Strange Little Cat)
Sternstunde ihres Lebens (ARD, 2014): TV film about German politician Elisabeth Selbert's struggle to have equal rights for men and women included in the constitution of the Federal Republic of Germany in 1946. You can view the film here and ARD have extra material about the film and equal rights in German here.