Fiction:

• Bleak House - Charles Dickens (I'd choose this over Great Expectations)
• If on a Winter's Night a Traveler - Italo Calvino
• The Shipping News - Annie Proulx
• Mrs. Dalloway - Virginia Woolf (I'd choose this over A Room of One's Own)
• The Tenant of Wildfell Hall - Anne Bronte
• The Golden Gate - Vikram Seth
• I, Claudius - Robert Graves

Non-fiction:

• The Right Stuff - Tom Wolfe
• Annals of the Former World - John McPhee

Plays:

• Travesties - Tom Stoppard
• Angels in America - Tony Kushner
• Faith Healer - Brian Friel

Poetry:

• Complete Poems of W. B. Yeats
• Complete Poems of W. H. Auden

With all due respect to The Hunger Games and The Help - they aren't classics.