To Kill A Mockingbird - (it's already been suggested but it's just so brilliant)
Of Mice And Men
For Whom The Bell Tolls - Hemingway at his absolute best.
Little Woman - (misleading title but) a truly great book.
The next few books aren't classics yet as they're still relatively new but I think they're destined to be held up as greats of their era.
We Need To Talk About Kevin - chilling, darkly humorous and thought provoking. I love this book.
The Northern Lights (Trilogy) - I first read these when I was twenty one. It was like reading the Chronicles Of Narnia for the first time... only better. Despite appearances these aren't just for kids. They're brilliantly written and in a word enchanting. If any of you have got kids, do them a favour and buy these books. All the praise Philip Pullman has had heaped on him for writing the series is well deserved.
All the aforementioned books have one mark of greatness in common. As soon as you've finished them, you'll want to start again. I will definitely reread all of them.
There is one other book I'd like to mention. The Aquariums Of Pyongyang is riveting. A shocking look into the gulags and concentration camps of North Korea. It's written Chol-hwan Kang, a survivor of the notorious Yodok concentration camp (he was sent there with the rest of his family when he was just nine years old).