As with my other lists, this isn't meant to be comprehensive, though I've added all the titles I could think of/find at the store browsing shelves in fiction. If you know titles I've missed, feel free to add them in the comments section.
This list encroaches on the Zombie reading list, so I only picked those titles that I thought showed the apocalypse/aftermath well.
Wastelands - John Adams, Ed.
Beyond Armageddon - Walter Miller, Ed.
Oryx & Crake; The Year of the Flood – Margaret Atwood
Ariel, Elegy Beach - Steven Boyett
Noise – Darin Bradley
Postman – David Brin
Armageddon's Children; The Elves of Cintra; The Gypsy Morph – Terry Brooks
World War Z – Max Brooks
Parable of the Sower; Parable of the Talents – Octavia Butler
Plague Year; Plague War; Plague Zone – Jeff Carlson
The Hunger Games; Catching Fire; Mockingjay – Suzanne Collins
The Passage – Justin Cronin
One Second After – William Forstchen
Alas, Babylon – Pat Frank
Go-Go Girls of the Apocalypse – Victor Gischler
Xombies: Apocalyptic Blues; Apocalypticon – Walter Greatshell
White Plague – Frank Herbert
Brown Girl in the Ring – Nalo Hopkinson
Children of Men – P.D. James
Cell – Stephen King
Left Behind – Tim LeHaye & Jerry Jenkins
I Am Legend – Richard Matheson
Chronicles of the Apocalypse: Species – Michael McBride
The Road – Cormac McCarthy
A Canticle for Leibowitz - Arthur Miller, Jr.
Homeland – Paul William Roberts
Last Light; Afterblight – Alex Scarrow
The Last Man – Mary Shelley
On the Beach – Neale Shute
Earth Abides – George Stewart
Y: The Last Man – Brian Vaughan
Day of the Triffids - John Wyndham
Deathlands - James Axler
Afterblight Chronicles: The Culled - Simon Spurrier
Afterblight Chronicles: School's Out - Scott Andrews
Additions from Commenters
Rot & Ruin - Jonathan Maberry
Sos the Rope; Var the Stick; Neq the Sword - Piers Anthony
Flood; Ark - Stephen Baxter
Exit Earth - Martin Caidin
Dies the Fire - S.M. Stirling
For other Apocalyptic Reading Lists, check out:
Read More Books' list
And for what's probably the most comprehensive list of Apocalyptic and Post-Apocalyptic fiction on the net, there's Exit of Humanity's list.
Oxford American has published a list of 10 great apocalyptic novels, finding some titles I've never heard of.
Skiffy and Fanty have a list of 10 Post-Apocalyptic novels written by women, with several titles new to me.