If you want to get really systematic about it, there's a list of 1,001 books you must read before you die -- although half the fun of a list like that is quibbling with it, and I personally think there's plenty on there I'd rather die than read (well, you know what I mean).
My own list of absolute must-read classics would only include books that are both "important" and also really enjoyable to read:
Don Quixote
The Iliad and the Odyssey
Some representative Shakespeare, although those are often more fun to watch than to read if you have access to good performances
Emma
Persuasion
Vanity Fair
Middlemarch
Gulliver's Travels
Tom Jones
The REd and the Black
Madame Bovary
Anna Karenina (I'm sure War and Peace is terrific, but haven't read it ...)
Crime and Punishment
Bleak House
David Copperfield
A Christmas Carol
Jane Eyre
Wuthering Heights
Dracula
At least a few of the Sherlock Holmes stories
The Age of Innocence
The Custom of the Country
Portrait of a Lady
Mrs. Dalloway
Huck Finn
The Grapes of Wrath
The Great Gatsby
A Child's Christmas in Wales
Claudine at School
The Sheltering Sky
The Leopard/Il Gattopardo
Invisible Cities
Out of Africa
As I Lay Dying
The Optimist's Daughter
A Delta Wedding
Gone with the Wind is worth reading because it's A) good trashy fun and B) a useful historical artifact. But it's extremely racist (one of the things that makes it a useful historical artifact), so proceed with caution if you're likely to be offended
To Kill a Mockingbird
In Cold Blood
A Death in the Family
We Have Always Lived in the Castle
The Big Sleep
Franny and Zooey
The Invisible Man
Couples
American Pastoral
Atonement
The Confessions of Nat Turner
Their Eyes Were Watching God
Hamilton Stark
Nights at the Circus
Wise Children
Tripmaster Monkey
You Bright and Risen Angels (very weird, not everyone's cup of tea)
The Electric Kool-Aid Acid Test
A Wild Sheep Chase
Catch 22
Slaughterhouse 5
Possession
The Amazing Adventures of Cavalier and Klay
The History of the World in 10 1/2 Chapters
I cannot recommend On the Road, Catcher in the Rye, Tropic of Cancer, The Naked and the Dead, and many other Important Books because I didn't like them.
