Oh man, I've got a bunch.
Emma - Jane Austen
Old Man & the Sea - Hemingway
Red Badge of Courage - Stephen Crane
The Red Pony - Steinbeck
Return of the Native - Hardy
Tess of the D'Urbervilles - Hardy
Wuthering Heights - Bronte
Metamorphosis - Kafka
Amerika - Kafka
The Trial - Kafka
The Castle - Kafka
plus I've probably read just about all of his short stories
Magic Mountain - Mann
Death in Venice - Mann
Siddhartha - Hesse
Demian - Hesse
On the Road - Kerouac
The Dharma Bums - Kerouac
To Kill a Mockingbird - Harper Lee
Suetonius
Tacitus
Inferno - Dante
Purgatorio - Dante
Paradisio - Dante
Huck Finn - Twain
Tom Sawyer - Twain
Turn of the Screw - James
White Fang - Jack London
Call of the Wild - Jack London
Johnny Tremain - Esther Forbes (dunno if that's considered a classic)
Alice in Wonderland - Carroll
Through the Looking Glass - Carroll
Three Sisters - Chekhov
Death of a Salesman - Miller
The Skin of our Teeth - Wilder
Our Town - Wilder
a lot of Shakespeare, mainly the tragedies
Long Day's Journey into Night - Eugene O'Neill
A Doll's House - Ibsen
The Importance of Being Earnest - Oscar Wilde
Picture of Dorian Gray - Wilde
The Glass Menagerie - Tennessee Williams
Heart of Darkness - Conrad
Crime & Punishment - Dostoyevskii
In Cold Blood - Capote
Iliad - Homer
Odyssey - Homer
Aeneid
As I Lay Dying - Faulkner
A Tale of Two Cities - Dickens
Great Expectations - Dickens
Ragtime - Doctorow
The Great Gatsby - F. Scott Fitzgerald
The Scarlet Letter - Hawthorne
One Hundred Years of Solitude - Marquez
1984 - Orwell
Animal Farm - Orwell
Gulliver's Travels - Swift
much of Vonnegut
Walden - Thoreau
Canterbury Tales - Chaucer
Dracula - Stoker
Frankenstein - Mary Shelley
I used this list:
http://www.thewritingtutor.biz/suggested_reading/APliteraturebyauthor.php as a memory guide. A lot of these were read in High School; I had an unbelievable AP English teacher, Kitty Lindsay.
A few I have on my list to read are Beowulf and Pepys.
Dang, that's a big list.