…at least, according to you!
I’m going to bypass such trivial works as The Great Gatsby and Moby Dick and go with:
A Prayer for Owen Meany, by John Irving
Fierce Invalids Home from Hot Climates, by Tom Robbins
The Blind Assassin, by Margaret Atwood
Motherless Brooklyn, by Jonathan Lethem
The Pigman, by Paul Zindel
This thread is also my sneaky way of compiling an interesting list for a new book-buying spree.
You sneaky devil!
None of my choices are anything like the books on your list but I’ll share them anyway.
The English Passengers by Matthew Kneale (historical)
Lonesome Dove by Larry McMurtry (western)
The Dollmaker by Harriett Arnow (Appalachian/WWII/family)
Fevre Dream by George R. R. Martin (vampire)
The Book of Joby by Mark Ferrari (coming of age/Arthurian)
Sure:
The Lord of the Rings by J.R.R. Tolkien
The Moon is a Harsh Mistress by Robert Anson Heinlein
To Kill a Mockingbird by Harper Lee
Silent Spring by Rachel Carson
A Short History of the World by Herbert George Wells (an excellent summary of world history up to around 1922)
Jim
The Autobiography of Malcolm X - Alex Haley & Malcolm X
Another Roadside Attraction - Tom Robbins
Fear & Loathing in Las Vegas - Hunter S. Thompson
Perfume: the Story of a Murderer - Patrick Suskind
And the Ass Saw the Angel - Nick Cave
The last four are just four very different examples of beautiful, invocative writing. The first is important for everyone to read, I feel.
There’s only one book in that category:
How to Live Forever.
Then you can take your time reading all the other ones. 
OK, seriously:
On the Origin of Species by Means of Natural Selection by Charles Darwin
*The Ancestor’s Tale *by Richard Dawkins
On Human Nature by E. O. Wilson
The Feynman Lectures on Physics by Richard Feynman (Three Volumes)
An Enquiry Into the Nature and Causes of the Wealth of Nations by Adam Smith
You didn’t say they had to be fiction.
In no particular order:
The Unvanquished by William Faulkner
Mother Night by Kurt Vonnegut
We Wish to Inform You That Tomorrow We Will Be Killed With Our Families by Philip Gourevitch
A Confederacy of Dunces by John Kennedy Toole
and…
I can’t think of a fifth one, and I have to leave now. So, uh, the OED?
A suggestion, tell us why we should read those books before we die. Why are those five books on your list so important? What kind of meaning do they convey?
Just making a list of books you like doesn’t really make me want to read them unless I think there’s something I could get out of them.
Just five? Shooting from the hip, I’d pick:
The Cry Of The Owl – Patricia Highsmith
Mildred Pierce – James M. Cain
Adventures of Huckleberry Finn – Mark Twain
The Art of Eating – M.L.K. Fisher
Zorba The Greek – Nikos Kazantzakis
Come back tomorrow–or indeed, in eve a few minutes–and I’ll probably give you five more, like:
The Unbearable Lightness of Being – Milan Kundera
Keep the Aspidistra Flying – George Orwell
The Grifters – Jim Thompson
Euclid’s Elements – Euclid of Alexandria
The Gulag Archipelago – Aleksandr Solzhenitsyn
Don Quijote de la Mancha – Miguel de Cervantes
Gulliver’s Travels – Jonathon Swift
The Spy Who Came In From The Cold – John le Carré
…et cetera, ad nausum.
Hell, the only proper way to answer this is that there are vastly more than five books you should read before you die. A coworker of mine once reported that her boyfriend/fiance had only read “for pleasure” four books in his life. That strikes me as being terribly sad.
Stranger
Douglas Adams- Dirk Gently’s Holistic Detective Agency
Robert Heinlein- Stranger in a Strange Land
Orson Card -Ender’s Game
Jerome Salinger- Catcher in the Rye
Jane Austin- Pride and Prejudice
Shakespeare - Complete Works
Dickens - Complete Works
Austen - Complete Works
Feynman - Surely you’re joking, Mr Feynman?
Tolkein - Complete Works (when it gets compiled into one volume).
Point of Impact - Stephen Hunter. Great action with cranky ol’ retired Marine sniper hunting down the guys that killed his dog.
Moonheart - Charles De Lint. Magic and mystery in the streets of Ottawa. Great escapism fantasy.
Time Enough for Love - Robert Heinlein. Because I couldn’t choose between all the great Heinlein novels
Band of Brothers - Stephen E. Ambrose. Miniseries on HBO (I think) based on this book. Follows 101st Airborne “E” company through Europe.
Neuromancer - William Gibson. Because this is the cyberpunk novel and what I sometimes dream technology could become
Catch 22 - Heller
Lord of the Rings - Tolkein
To Kill a Mockingbird - Lee
Slaughterhouse 5 - Vonnegutt
Candide - Voltaire
I’m glad you kept it to five, but it’s a hard restriction to keep! How can I not mention Salinger, Roth, Updike, Darwin, Faulkner, so many more…
Flowers For Algernon - Daniel Keyes
Good Omens - Terry Pratchett and Neil Gaiman
Cat’s Cradle - Kurt Vonnegut (other candidates: Galapagos, Sirens of Titan, Player Piano)
Othello - William Shakespeare (other candidates: Macbeth, Romeo and Juliet, Much Ado About Nothing, A Midsummer Night’s Dream)
The Demon-Haunted World - Carl Sagan (I haven’t actually read this one (not for want of trying), but if even half of what I’ve heard about it is true, it belongs on this list)
The Sot-Weed Factorp by John Barth
Replay by Ken Grimwood
Gravity’s Rainbow by Thomas Pynchon
McTeague by Frank Norris
Catch-22 by Joseph Heller.
The Turner Diaries, Tommyknockers, Jonathan Livingston Seagull, and any two of the Left Behind books.
That way, dying won’t seem so bad.
Oh sod it, how did I forget this one? Strike that Sagan book that I haven’t even read from my list, substitute Replay.
A Million Little Pieces, by James Frey
Natural Cures “They” Don’t Want You To Know About, by Kevin Trudeau
Find It, Fix It, Flip It!: Make Millions in Real Estate–One House at a Time, by Michael Corbett
Godless: The Church of Liberalism, by Anne Coulter
If I Did It, by O.J. Simpson
[spoiler]Okay, here the the real ones.
At least one tragedy and one comedy by Shakespeare: Hamlet and As You Like It
All Quiet on the Western Front
To Kill a Mockingbird
Pride and Prejudice
A Soldier of the Great War[/spoiler]
**Miller, **you forgot Love Story.
koeeoaddi, you forgot the first edition of* Everything You Always Wanted to Know about Sex (But Were Afraid to Ask)* (or as I called it, The Big Golden Book of Lies).
I believe “repressed” would be the more accurate term.
I’m going to cheat and include one series:
The Oz Books, by L. Frank Baum
Little Women, Louisa May Alcott
Gone with the Wind, Margaret Mitchell
Atlas Shrugged, Ayn Rand
Gift of Fear, Gavin de Becker