As many of these as possible
More selectively (still using Bloom as a guide), the major works of: Shakespeare, Cervantes, Montaigne, Milton, Tolstoy, Vergil, Augustine, Dante, Chaucer, Plato, St. Paul, Goethe, Dr. Samuel Johnson, Nietzsche, Proust, Kafka, Ibsen, Chekhov, Swift, Austen, Hawthorne, Melville, Woolf, Emerson, Dickenson, Eliot, Wordsworth, Shelley, Hugo, Baudelaire, Homer, Joyce, Twain, Faulkner, Whitman, Fitzgerald, Flaubert, Borges, William Blake, W.B. Yeats, Dickens, and Dostoevsky all jump out at me at this exact moment (though I really have no clue if that's a good shortened list).
When asked to choose the most critical four books, Bloom chose:
1. The collected works of Shakespeare
2. The Divine Comedy - Dante
3. The Canterbury Tales - Chaucer
4. The Iliad - Homer
(his fifth would probably be Don Quixote)