A really weird but thought-provoking one is called The Gone-Away World, about a world where the fallout from very special bombs have had some really weird consequences. And no, there's no zombies or mutants as far as I remember. It's weirder than that.
The manga (and the anime series it was based on) Neon Genesis Evangelion is very much a post-apocalyptic story. It starts off as a giant robots versus giant monsters story...and then goes off the deep end, with discussions about the nature of humanity and evolution, as well as making sure that half the bloody cast have more than one skeleton in the closet. Disturbing, but thought-provoking.
You've already mentioned The Stand, SisterJennifer. Bugger, I was gonna mention that...
Oh, I know! Ben Croshaw, AKA Yahtzee of Zero Punctuation fame, wrote a post-apocalyptic book set in Brisbane called Jam. It's about what happens when the entirety of Brisbane ends up several feet deep in what seems to be carnivorous strawberry jam. While many elements of the book are a dark comedy, it also pulls apart many of the tropes used in post-apocalyptic stories.