While I've been on the subject of Albinoni/Giazotti's famous Adagio, I came across an extensive list here of classical music used as part of a soundtrack and/or featured in movies.
While Hollywood usually employ composers specifically to write the soundtrack music for a film there are people who work on films, who's exclusive task is to compile music appropriate for a particular scene or setting. These people are often credited for their work, and some of them have even won awards for their work. They are known in Hollywood as a Compiler.
And then of course there are classical composers who write music for film. The first person who comes to mind is John Williams, who wrote the scores for many Steven Spielberg and George Lucas films (among others), including the title music for the Star Wars Films, and the memorable Jaws Theme.
Here's Wiki's list of film score composers.
Among that list are classical composers who have also composed works outside of film, including Richard Addinsell (1904-1977), who wrote his famous Warsaw Concerto for the 1941 film Dangerous Moonlight.
The late film director Stanley Kubrick compiled the music for his 1968 Space adventure 2001: A Space Odyssey, which featured works from Johann Strauss II (1825-1899): On The Beautiful Blue Danube Waltz and Richard Wagner (1813-1883)'s Also Sprach Zarathustra.
Here's a list of what The Guardian UK considers the 50 greatest film scores of all time.