I know you said that you’ve read many of the older books, but just in case it slipped under your radar (because I don’t often see it mentioned in threads like this), I highly recommend The Death of Grass by John Christopher.
For newer novels, Marcel Theroux’s Far North was an interesting read - entertaining and lonely, which is what I prefer in a dystopian/PA novel. 
Are you aware Palmer finally wrote the sequel? Tracking was serialized in Analog magazine in 2008. It was supposed to then be published in book form but the publisher went bankrupt and nobody else has picked up the rights yet.
My father in law recommended Without Warning and its sequel After America by John Birmingham. I read a bit and seemed to be fun, action-packed type books. North America basically gets rubbed out by a cosmic eraser and everybody scrambles to put the pieces back together.
After a recommendation here for a good zombie novel, I gave my step-son Day By Day Armageddon by J.L. Bourne. He seems to have loved it (while never admitting that he actually liked such a lame gift as a book). He also liked World War Z: An Oral History of the Zombie War and The Zombie Survival Guide by Max Brooks, which I suppose you’ve probably already read, Lucky Mike. I found both readable but thought the first one was written in something like a monotone-- especially compared to Studs Turkel’s The Good War, to which Z owed an obvious debt, and Guide was just OK.
Maybe an odd recommendation, but I’ve always been fond of Poul Anderson’s Brainwave, where life on Earth is thrown out of completely joint by a sudden, apocalyptic, sharp… increase in IQ.
Soft apocalypse by Will McIntosh
I’m a fan of John Wyndham. The Kraken Wakes and The Day of the Triffids may fit the bill. The Triffids sequel The Night of the Triffids by Simon Clark is OK too.
Directive 51 and Daybreak Zero by John Barnes. There is a third novel in the series that I haven’t read yet - The Last President.
The Last President keeps being delayed; it’s currently due in September.
The 3rd** John Birmingham** book just came out in paperback, The Angels of Vengeance.
Quite liked Soft Apocalypse by Wil McIntosh as mentioned by turner above; Hitchers is also very good but less apocalyptic…
I’m not a Harry Turtledove fan, but I’ve enjoyed both his Supervolcano books, Eruption and All all Down more than I expected. Yellowstone erupts and blankets several states with thick ash. No omniscient overview, it’s all told from the point of view of characters (often related) dealing with things as they unfold over time.
Brian Francis Slattery just won the Philip K. Dick award with Lost Everything, which I’ve not read yet, but looks interesting.
Life As We Knew It by Susan Beth Pfeffer. An asteroid hits the moon and knocks it closer to Earth. The results are catastrophic. Reading it, I felt like the events were really happening around me. For weeks afterward, every time I looked at the moon, I got chills.
It gives a realistic portrayal of the teenaged protagonist chafing at the constraints imposed by the disaster (no electricity, dwindling food supplies, nuclear winter-like weather conditions, her friends dying). She doesn’t automatically shift into “put on a brave face” mode: she feels fear, sorrow for being separated by her loved one, anger for her lost future, and shame. She occasionally lashes out at her mother and her friends for the choices they make. You can understand her frustrations as her world grows narrower and her struggle to survive becomes more daunting.
I might not be describing this character accurately: she’s not a brat. She’s not perfect, and that makes the story more compelling, that there are psychological as well as physical implications of the apocalyptic event.
Life as We Knew It sounds a little like Age of Miracles, a YA end-of-the-world novel about the planet slowing and the days growing longer. The protagonists sounds similar: teenage girls who just want to be teenagers. I liked Age of Miracles- I’ll have to look into Life as We Knew It.
Perhaps not quite exactly the kind of post-apocalyptic fiction you’re looking for, but check out S.M. Stirling’s Emberverse series. You won’t be sorry.
How about Earth Abides, by George R. Stewart? It’s pretty old, so maybe you’ve read it, but I searched through a lot of Half Price Books stores before I finally found a copy at an estate sale for 50 cents.
I loved this book, details and all.
When then book reveals that some remnant of the US government did survive, it’s simultaneously amusing and terrifying to find out that the president was a cabinet secretary (don’t remember what the position would have been called back then, but HUD Secretary, now) who survived because she was out inspecting some government-backed housing project while everybody else in the chain of succession was vapourized!
You have to read the other two to find out where it goes and how it ends, and to be inspired to see who they cast with Jennifer Lawrence in the movies!
It might be hard to enjoy that third book, though …
Oh, Post-Apocalyptic novel! What this thread is about! I was wondering when Palmer wrote Powered Armour novel. I just finished Old Man’s War by John Scalzi and looked back through Starship Troopers again for some quotes for another message board.
How about Christopher’s Tripod books: The White Mountains, The City of Gold and Lead, and finally The Pool of Fire? I enjoyed reading those years ago, and really wished they would have collected the serialized comic adaption that appeared in Boy’s Life magazine when I was a scout.
Those might not qualify, as the apocalyptic destruction is the result of an alien invasion and occupation, which pushes the genre too much into science fiction.
Darn it! I was going to suggest Lucky Mike read World War Z before Brad Pitt has a chance to ruin it.
Okay so I am new and havent read the rest of the thread so may be repeating myself but I’ll just write a list of my favourites as I’m a total apocalypse nerd
The Death of Grass by John Christopher
A Canticle For Leibowitz - can’t remember the author off the top of my head but this is an incredible book
The Day of the Triffids, The Kraken Wakes and The Chrysalids by John Wyndam
Earth Abides by George R Stewart
World War Z
The Stand by Stephen King
The Passage by Justin Cronin
1984 obviously
The First and Last Men by Olaf Stapledon
There are probably more but those are what immediately spring to mind!
I also have an anthology of apocalyptic short stories called Wastelands, pretty sure I bought it on Amazon. Also just saw you were looking for modern stuff, my apologies! Most of the best science fiction was written in the fifties imo but now I’ll be interested to hear what other people suggest.
“Scarlet Plague” by Jack London (which as an added bonus has the apocalyptic plague indicated in the title occurring this year) http://london.sonoma.edu/Writings/Scarlet/
Wolf and Iron by Gordon R. Dickson.
Dust, by Charles Pellagrino
Blood Music by Greg Bear
Hammer of God also Greg Bear
When Worlds Collide (a classic in the genre)
Empty World, by John Christopher
Seed; Rob Ziegler
Really enjoyed The Passage and The Twelve by Justin Cronin. Looking forward to the third installment.
I’ll nominate the Chaos Walking series by Patrick Ness. First book is The Knife of Never Letting Go. It takes place on an alien world where a virus has killed all the women and made the men into psychic beacons, constantly broadcasting their every thought to everyone nearby. Depending on your point of view, it’s more science fiction than post-apocalyptic, but the writing is fantastic.
I liked that one.
And older one that you may have missed that I like is Hiero’s Journey. Although it’s really post apocalyptic, long after the war that destroyed civilization.