I am not certain about all movies, thus I will post this as a community wiki and hope the remaining gaps will be filled. I think, they did not play the exact soundtracks, but rather similar music that references the originals.
I used this video to roughly note the times.
Here is my attempt:
- [2:25] ? - The music style is clearly like in a silent film, but I am not sure, whether it belongs to a specific film, or just the genre.
- [3:25] [Forrest Gump]2
- [3:45] [Zorro]3 (the film or one of the series?)
- [3:55] [Titanic]4 (the 1997 version)
- [4:22] [Snow White]5 (probably the Disney version from 1937)
- [4:45] [King Kong]6 (probably the 1933 version)
- [5:05] [Avatar]7
- [5:30] [Star Wars]8 (yeah well, just pick one ;) )
- [5:40] [Mission Impossible]9
- [5:45] ? some Russian film with regional background ?
- [6:08] Same music as Masha And The Bear's First Episode 11, hence their telling their own story