A friend of mine recently brought up The Grapes of Wrath which I read a couple of times but years ago, anyway I thought of the chapter about used cars. Could stand alone.
The Hotel New Hampshire by John Irving. “Holy cow, you kilt State-O’ Maine.”
Isn’t there an actual short story in The Tommyknockers? Something about the TV talking to a woman?
It’s somewhat common for a novel to be put together from short stories:
Michener’s style is like that. The chapter “The Watermen” from the novel “Chesapeake” or “The Cowboys” from the novel “Centennial.”
The first chapter of Andreas Eschbach’s The Carpet Makers was actually published as a short story. I’m pretty sure it was not designed to be one, but it stands completely on its own outside the novel, while still being a key part of the novel. There are probably other chapters that can stand alone, too.
It wasn’t uncommon in SF for authors to turn short works into novels. Anne McCaffry’s “Weyr Search” became a part of her Dragonflight, for instance.
John Barry’s The Sot-Weed Factor is filled with people telling stories to each other, many of which can stand alone.
Two Ray Bradbury books–The Martian Chronicles and The Illustrated Man–always seemed like hey were in some weird niche between an anthology and a novel.
The OP mentioned John Irving. It’s been years since I read “The World According To Garp” but I seem to recall a couple of chapters that were supposed to be short stories written by Garp.
Also his Dandelion Wine.
The first chapters of the following books would be good short stories:
Snow Crash by Neal Stephenson.
This Body’s Not Big Enough for Both of Us by Edgar Cantero.
John Dies at the End by David Wong.
A chapter in Born to Trot by Marguerite Henry about a runaway horse in a trotting race.
Actually, a number of children’s books have chapters that would work in this way, and I read them in classroom readers before finding the actual books. “The Back of the Bus” by Elizabeth Enright is from The Four-Story Mistake and “Little Vic” by Doris Gates is the chapter “Thunder on His Neck” from Little Vic, for example.
A number of chapters in Serge Storms books by Tim Dorsey.
334 by Thomas M Disch sprang immediately to mind. It’s on the list. Impressive.
j
Dandelion Wine, also.
I’ve seen the brilliant final chapter of Evelyn Waugh’s A Handful of Dust printed, with minor tweaks, as “The Man Who Loved Dickens.” In horror fiction anthologies.
As a matter of fact, I have definitely seen the early chapter of Dandelion Wine — in which a little old lady runs home from the movies because she’s afraid the local serial killer has targeted her — as a short story in one of the Alfred Hitchcock suspense anthologies. No idea which one (there are dozens) or what it got retitled.
The chapter from The Stand that explains the fates of several people unaffiliated with the plot.
Ukulele Ike, you’re thinking of “The Whole Town’s Sleeping”:
Orphanogenesis is the first chapter of Greg Egan’s Disaspora; it’s also been published as a short story http://www.isfdb.org/cgi-bin/pl.cgi?59085
The Secret Pilgrim by John le Carré is called an “episodic novel.” Its 11 chapters are 11 different stories. Recommended!
If torn between novel and short story, why not read novellas? 
There are several great authors — Dostoevsky, Hemingway, Steinbeck, London, Melville — whose novella(s) I love, but whose long novels I can barely finish.
“Cranford” by Elizabeth Gaskell is a loosely-connected series of episodes, which makes it a natural for adapting to TV (as it has been multiple times). The chapter “The Panic” where the town is hit by mass hysteria over mysterious prowlers would make a good short story.
Heinlein’s Time Enough For Love.
Barth?
“The Starfolk: A Fable” in Carl Sagan’s The Cosmic Connection.
L. Sprague deCamp and Lin Carter adapted the Conan the Barbarian screenplay into a novel. (Yes, the Schwarzenegger flick.) The scene where Conan’s father teaches him the Riddle of Steel could stand on its own.
Moby-Dick has a number of chapters which could stand alone, maybe not as short stories, but as essays on various topics. Likewise War and Peace.
The Vicomte de Bragelonne: Ten Years Later, Alexandre Dumas’ second sequel to The Three Musketeers, contains a lot of chapters that have no real connection to the main story. It is a sprawling, meandering book. It takes a long time for Dumas to make up his mind which storyline to follow. (You have probably heard of the finale: It’s usually published as a separate volume, under the title The Man in the Iron Mask.)
As is commonly known, Franz Kafka published very little during his lifetime, and all his three novels were published posthumously. But one chapter of the the novel “Amerika” (also known as “Der Verschollene”) had been already published during his lifetime as a short story under the title “Der Heizer” (“The Stoker”).