Must read classics?

Middlemarch.. I just re-read and it is extraordinary...
Anna karenina... Brilliant
Anything by Trollope
Bleak house

20th c
Great gatsby
Handmaid's tale
Dubliners

That should keep you going for a bit!

War and Peace - seriously, best book ever.
Crime and Punishment.
The Brothers Karamazov.
These are my favourite books of all time.

If you haven't really read any, you may like to start with something a bit lighter.

I would suggest
Silas Marner
The Mill on the Floss
Tess of the D'Urbervilles
Far From the Madding Crowd
Wuthering Heights

For slightly more modern books, try The Grapes of Wrath, one of my very favourite books.

I'm sure there are lots of others, and that we'll all give different suggestions. How lovely to have a job where you're allowed to read.

Jane Eyre
Catch 22
Heart of Darkness
Freedom or Death
Beowulf
The Iliad & The Odyssey
Shakespeare

Remember, just because it's a classic doesn't mean you have to wade through it if it's not doing it for you (Catch 22 fail - several times - here) - reading, unless you're doing an English literature degree, is meant to be for pleasure (I mean, hopefully it should be that even if you're doing an Eng lit degree, but the latter will require some set texts that you don't warm to).

War and Peace
Madame Bovary
Anything by Jane Austen
The Decameron (essentially short stories so great for reading at work)
The Grapes of Wrath
The Woman in White
The Red and the Black

I don't do classics as such, but I think Jonathon Livingston Seagull,1984, Down and Out in Paris and London, and The Age of reason are ones that I have read and actually got something from.

I want to read The call of the wild.

Brave New World
A Tale of Two Cities
The Leopard
Guy de Maupassant short stories
Contempt by Alberto Moravia
The Twelve Caesars
The Tin Drum
The Outsider, and The Plague
Things Fall Apart
The Icelandic Sagas
Greek Myths

Not all pre-20th century classics, but all good 'uns

To Kill a Mockingbird
Rebecca
Jane Eyre
The Woman in White
Cold Comfort Farm
I Capture the Castle
The Monk
The Razor's Edge (Somerset Maugham)

PMSL at the thought of Silas Marner and Tess of the D'Urbervilles being described as lighter!

What's the cut-off point for something being a 'classic'?

Animal farm
Lolita
One flew over the cuckoo's nest

I'd second the Monk, The Woman in White and Jane Austen recommendations and I'd add:
Dracula
The Private Memoirs and confessions of a Justified Sinner by James Hogg
The Moonstone
The Awakening
Dr Jekyll and Mr Hyde
All Oscar Wilde plays along with the Picture of Dorian Grey
Paradise lost

20th C recs would be The Bloody Chamber by Angela Carter
Midnight's Children Salman Rushdie
The God of Small Things by Arundhati Roy
The Great Gatsby

That'll do for now

having thought some more I'll add

The Remains of the Day - Ishiguru
Wolf Hall/Bringing up the Bodies - Hilary Mantel
Disgrace - J M Coetzee
and for sheer fantastic-ness, though I doubt anyone would call it a classic of literature, Ken Follet's The Pillars if the Earth

Trollope, especially A Small House at Allington and The Eustace Diamonds

Vanity Fair

Dickens Bleak House

Sons & Lovers
To Kill A Mocking Bird
Tess of the D'Urbervilles
My Antonia / The Song of the Lark (Willa Cather)
The Big Sleep / The Long Hot Summer (William Faulkner)
Breakfast At Tiffany's
Frost In May

Daniel Defoe is great. Not just Robinson Crusoe, but also Moll Flanders (what a heroine!) and A Journal of the Plague Year, v. early reportage/fiction mash-up, and fascinating. I keep meaning to read Roxana and his non-fiction essays, but haven't got to it yet.

Oroonoko, by Aphra Behn (first English novel to feature a black central character, I think)

Dumas-Three Musketeers, Count of Monte Cristo, Man in Iron Mask, etc? I don't actually ever manage to finish Dumas, but worth a try.

I like Austen a lot, but I think Elizabeth Gaskell is better: North and South, Wives and Daughters, Cranford etc

C19th Ghost stories I love: M.R. James, Edith Wharton, Henry James.

Short stories by people you don't necessarily associate with them: years ago I read Chekov's, and Pushkin's, and enjoyed them enormously.

Buddenbrookes, by Thomas Mann.

Christ Stopped at Eboli by Italo Calvino.

Gosh, there are so many.

Aw, C&P. I remember choosing that as my Y9 English prize to be all highbrow, but I really got into it.

She Came to Stay, Memoires d'une jeune fille rangee (sorry no accents and probs wrong sp) and The Mandarins
My Mother's House by Colette, all of her stuff anyway

Virginia Woolf- The Waves

Oh Maupassant- I still can't read Boule de Suif without having a good old howl!

Jude the Obscure - had to study this for A level but loved it and have reread it several times since.

One more to add-

Lysistrata.