Bach has written a huge body of keyboard music that ranges from "easy peasy" (Anna Magdalena) to "inhuman" (the ol' prelude & fugue).
A significant part of it is both popular with public performance and recording (by a number of big name players as well - think Gould, Joao Pires) and part of the standard "intermediate" (Grade 5-7) piano curriculum - in other words something most students will play at some point or another.
Everybody, not just future virtuosos, your cousin who is in med school but has been taking piano lessons for 4 or 5 years as well.
Is there anything else like that?
Especially from the classical period proper?
I can think of a few examples from late Romanticism/early 20th century - but that I know of, Rachmaninov's works are mostly virtuoso pieces, Debussy wrote either virtuoso pieces or beginner-intermediate pieces that people that are not piano students rarely know, Bartok - well, Bartok's piano works are fairly obscure anyway.
Is the intersection between "pieces that students play" and "pieces that great players/really proficient amateurs play" really limited to Bach?