The Death Of Ivan Ilyich sits at the juncture between European 19th-century moralist realism and the beginnings of modernism, this particular strain of which would find full flower in existentialism.
Examples of the former include Tolstoy's earlier novels Anna Karenina and War and Peace, and Emily Brontë's Wuthering Heights. F. Scott Fitzgerald's The Great Gatsby deals with many of the same themes as Ivan Ilyich, transposed to 1920s New York. Pixar's movie Up is quite similar as well, though much more optimistic.
Works that relate to the more spiritual side of Ivan Ilyich include Albert Camus' The Stranger and Henry James' The Wings of the Dove. Gustav Mahler's song cycle Das Lied von...