Classic literature is one of my favorite things and I have a ton of suggestions. The following list is of authors followed by their works I recommend.
Various: The Bible.
Homer: the Iliad, The Odyssey.
Unknown: The Epic of Gilgamesh, Beowulf.
Ovid: Metamorphoses.
Virgil: the Aeneid.
Dante Alighieri: The Divine Comedy.
Miguel de Cervantes: Don Quixote.
Geoffrey Chaucer: Canterbury Tales.
Alexandre Dumas: The Three Musketeers, The Count of Monte Cristo.
Victor Hugo: Les Misèrables, The Hunchback of Notre Dame.
Washington Irving: The Legend of Sleepy Hollow, Rip Van Winkle.
Lewis Carroll: Alice's Adventures in Wonderland.
Charlotte Bronte: Jane Eyre.
Emily Bronte: Wuthering Heights.
Louisa May Alcott: Little Women.
Bram Stoker: Dracula.
Mary Shelley: Frankenstein.
Robert Louis Stevenson: Dr. Jekyll and Mr. Hyde, Treasure Island.
Jules Verne: Around the World in 80 Days, Journey to the Center of the Earth, 20000 Leagues Under the Sea.
L. Frank Baum: The Wonderful Wizard of Oz.
Jane Austen: Emma, Northanger Abbey.
Arthur Conan Doyle: The Adventures of Sherlock Holmes, The Lost World.
Fyodor Dostoevsky: Crime and Punishment.
Leo Tolstoy: War and Peace.
Charles Dickens: A Tale of Two Cities, Great Expectations, A Christmas Carol, Oliver Twist, David Copperfield.
Mark Twain: Adventures of Tom Sawyer, Prince and the Pauper.
H.G. Wells: War of the Worlds, Island of Dr. Moreau, From Earth to the Moon, The Invisible Man, The Time Machine.
Gaston Leroux: The Phantom of the Opera.
John Steinbeck: Of Mice and Men, The Grapes of Wrath.
Jack London: Call of the Wild.
Margaret Mitchell: Gone with the Wind.
Hariett Beecher Stowe: Uncle Tom's Cabin.
Emile Zola: Germinal.
Frank Norris: McTeague.
Herman Meville: Moby Dick.
And I also suggest Fairy Tales because they are always pleasant to read. The stuff by the brothers Grimm and Hans Christian Andersen.