1)There is a large but finite number of tones in the classical system of music, and a large but still finite number of combinations of those. If you want a melody n notes in length restricted to one octave, you have 12ⁿ possible combinations, and not all of those combinations might be available under the tonal system Mozart and Beethoven worked with. Even after you expand the possibilities to account for different durations of the tones (whole notes, half notes, etc.), allow for extension beyond the octave, etc., you still end up with a finite number of possible combinations.
So the wonder should not be that composer A wrote a piece of music which seems to borrow from Composer B, but that the seeming borrowing does not happen more often.
2)Perhaps Brahms, in that famous passage from his First Symphony, was actually quoting Mozart, not Beethoven.
3) For a 20th century analogue, I would give you Shostakovich's 14th Symphony, in whivh one passage seems a clone of a passage in Bartok's Concerto/Sonata for 2 Pianos and Percussion.
