I'm not sure these are classics, but they are good. You must read C. S. Lewis' science fiction trilogy: Out of the Silent Planet, Perelandra and That Hideous Strength. It's not terribly science fictiony, like star trek or something, so even if you don't normally like science fiction, it is good. And if you haven't read the Cronicles of Narnia, you must. Then there's The Phantom of the Opera by Gaston Leroux (sp?) and The Picture of Dorian Gray by Oscar Wilde.
There's no point in being grown up if you can't be childish sometimes. -the Doctor