I love Aristophanes and Herodotos. And I really like Hamlet and Macbeth. And I'll read Austen any chance I get. Same with Woolf, really. Or Dumas. Or Wodehouse. I am writing my PhD on Dickens, so I suppose I'll have to mention him. And Thackeray and Stevenson. I quite like some of Zola. There is too much to mention. I real a lot of "canon" literature.

Edit: the more I think about this, the more books I feel that I should enter. There are so many good ones. Starting with Homer (Gilgamesh was alright, but not something I feel an immediate urge to re-read), on to Sapho, Aeschylos, Sohpocles, Plato, Xenophon, then Catullus, Vergil, Ovid. The mystery plays of the medieval period are worth your time. Geoffrey of Monmouth, Dante, Boccaccio, Chaucer, Cervantes' Don Quixote, Shakespeare, and Aphra Behn, Michel de Montaigne, Moliére, Racine, Fielding, Swift, Laurence Sterne, Goethe's Elective Affinities (not the tragic romantic stuff), Pope, Blake, Baudelaire, Lewis Carroll, Jules Verne, Nietzche (oh, my god, Nietzsche... or are we only talking about fiction here?), Ibsen and Strindberg, Henry James, Stevenson, Oscar Wilde, Thomas Mann, Gaston Leroux, Tolstoy, Dostoyevsky (within reason), Gogol, Bulgakov, Kafka, Joyce, Woolf, Proust, Walter Benjamin, Huxley, Orwell, Beckett, ... and with that I think we have reached the end of what I am comfortable calling a "classic". Although I will emphasise that I am associating wildly, and it is quite possible that I have forgotten someone I really like.

Hmm. If you are not used to reading non-contemporary books, I think Dumas or Wodehouse, possibly Austen (but I think possibly that works better if you are a girl) is a good place to start, mainly because the difference will not be so great. Stevenson is always great. Or, you know, Conan Doyle's Sherlock Holmes stories. Or Poe. Those are a good place to start because they are not terribly challenging.

The same goes for Tolstoy. I am always amused by how War and Peace is touted like this difficult, intellectual novel when it is really a soap opera. It is interesting, and it is fun to read (if you get through the periods of thoughts on history, but those are short).