McCarthy’s The Road is the definitive post-apocalyptic novel, and one my favourite books.
Atwoood’s Oyrx and Crake is fantastic, but it’s a not a pure post-apocalyptic novel. It’s really a dystopian book, and most of it focuses on the life of the protagonist and his involvement in the collapse of society. The sequel, The Year of the Flood, was also very good.
The Gone-Away world - Nick Harkaway. Shades Wodehouse mixed with some pretty interesting post-apoc imagery. At the very least, you are introduced to the concept of Car-fu. It’s exactly what it sounds like.
A cantical for Leibowitz - Walter M. Miller Jr. The original post-apoc fiction.
Lucifer’s Hammer - Larry Niven and Jerry Pournelle. A lot of Post-apoc fiction sets it with the apocalypse happening sometime in the past. Lucifer’s Hammer sets it right after the event, one of the few that does so I believe.
Tromik already mentioned The Road by Cormac McCarthy. One of his best works. It’s short, but packed with meaning, poetry and imagery.
Hiero’s Journey–Sterling Lanier. Somewhat obscure today and hard to find, but this book was pretty much THE inspiration for Gamma World and is very enjoyable.
I actually don’t remember if I’ve read anything in that direction except The Stand (multiple times). I actually liked, but didn’t love it. When thinking about it, I would actually also like to include works comparable to Kings The Mist (humans still fighting the apocalypse).
A Canticle for Liebowitz by Walter M. Miller, Jr., (why hasn’t that been mentioned in the thread yet?) is great for getting the sense of society recovering from the blast over many generations. He also edited a great anthology back in the '80s called Beyond Armageddon. I think that’s where I first read Bradbury’s “There Will Come Soft Rains”, which was so awesomely alluded to in Fallout 3.
Otomo’s Akira is great for getting the sense of society recovering from the blast after about twenty years later, then about three seconds later.
Most of the best ones have been mentioned. Personal favorites include The Stand (get the expanded, most recent version), Canticle for Liebowitz, Alas Babylon, On the Beach, and The Road. I can only somewhat recommend Lucifer’s Hammer at this point because it contains a ton of dated references for a current reader.
Others to consider:
Earth Abides - worth reading because its very realistic and the story covers both the immediate post-apoc but also basically the rest of the main characters life.
Dark Tower series - not fully post-apoc but enough to keep you interested if that is your thing, though not all the books in the series are equally deep in that aspect of the world.
Warday - a mid-80s “travelogue” of a couple of guys traveling around the US after a “limited” nuclear exchange between the US and Soviets. Very much focused on the real effects of even a limited nuclear apocalypse.
Do your self a favour and chek out The Judas Syndrome by Michael Poeltl. It’s the quintessential Apocalyptic story. It’s also a trilogy of which two are currently available and the third slated for a late 2011 release.