Mythology

Neil Gaiman's Norse Mythology stories of Thor and Loki (Available in the classroom in hardcover or online at this link.)

Crackling Mountain: Japanese myth about the tanuki (tanooki), the magical raccoon-like creature that explains why Super Mario wears a tanuki suit to fly. WARNING: disturbing content.

Neil Foster Macphail's modernizations:
Jason and the Argonauts (entire novel about a ship full of demigods meeting monsters and dangers. Individual chapters work as short stories.)
The Harpies
A Royal Bout
Stealing the Golden Fleece
Sea Pursuit
The Sirens
Talos the Brass Giant
Betrayal in the Night

The Odyssey
The bloody conclusion to Homer's Odyssey, in which Odysseus takes on a hall full of suitors: Slaughter in the Hall

Beowulf the Monster Slayer
Beowulf and the Monster Grendel
Beowulf Faces Grendel's Mother
Old Beowulf and the Dragon

Misc.

"Lesser Evil," Andrzej Sapkowski's story that the first episode of the TV show The Witcher is based on.

"Heorot" (Jim Butcher's modern Beowulf, with a battle wizard in Chicago)

Speculative Fiction

Star Trek:
Arena (trapped on a planet with a dangerous lizardman)
The City on the Edge of Forever (time travel to the 1930s)

Doctor Who story (Matt Smith Doctor and Amy Pond) by Neil Gaiman:
"Nothing O'Clock"

Orson Scott Card's original short story version of "Ender's Game"

Isaac Asimov robot stories:
"Runaround" (explorer robot is malfunctioning)
"Satisfaction Guaranteed" (woman has crush on lifelike house robot)

Time Travel:
Ray Bradbury: "A Sound of Thunder" (hunting dinosaurs)
Robert A. Heinlein: "By His Bootstraps" (annoyingly repetitive mindgame)

Fantasy/Horror/Mystery:
Edgar Allan Poe's "The Tell-tale Heart" (murder)
Edgar Allan Poe's "The Cask of Amontillado" (murder)
Edgar Allan Poe's "The Purloined Letter" (Poe invents the detective story)
Sir Arthur Conan Doyle's "The Speckled Band" (Doyle continues the detective story with his "Sherlock Holmes" character solving a mysterious murder)
Neil Gaiman: "We Can Get Them For You Wholesale" (a chance to have anyone you wish killed supernaturally)
Neil Gaiman: "The Truth Is A Cave In the Black Mountains" (an odd journey)
H.P. Lovecraft: "The Call of Cthulu" "The Colour Out of Space" (horrible forces wreck stuff)
Robert E. Howard's Conan the Barbarian stories (swordsman kills horrible Lovecraftian forces)
Robert E. Howard's "Tower of the Elephant" Conan story
L. Sprague De Camp's "The Thing In The Crypt" story of young Conan's first adventure.
Dungeons & Dragons Dragonlance stories
Anne McCaffrey's "The Smallest Dragonboy" (young teen gets a pet dragon to raise and one day ride)

Other:
Ray Bradbury's "The Veldt" (children's virtual reality jungle bedroom)
Poul Anderson: "Duel On Syrtis" (human big game hunter hunts alien on his own planet)
Stephen King: "The Jaunt" (family teleportation trip goes horribly wrong)
Mike Resnick's "Old Macdonald Had a Farm" (future bioengineered meat farm)
Neil Gaiman's "And Weep Like Alexander" (and uninventor)
Lena Coakley's "Mirror Image" (twin teenage girl gets a "full-body transplant" after a car accident leaves only her brain intact. Twin is jealous of new body.)

"Traditional High School English" Short Stories
(not speculative fiction, or remotely epic, folkloric nor mythic. Comparatively low imagination required.)

Ernest Hemingway's "The Short, Happy Life of Francis Macomber" (man takes his wife lion hunting. She may be cheating on him.)
Ambrose Bierce's "An Occurance At Owl Creek Bridge" (civil war soldier is to be hanged)
O. Henry's The Gift of the Magi (a poor couple at Christmas)
Shirley Jackson's "One Ordinary Day With Peanuts"
Shirley Jackson's "The Lottery" (kind of The Purge)
James Thurber's "The Secret Life of Walter Mitty"
Merna Summers' "The Skating Party" (which sister to marry?)
Hugh Garner's "The Father" (drunk dad)
D.H. Lawrence's "The Rocking Horse Winner" (sick kid)
Charlotte Perkins Stetson's "The Yellow Wallpaper"
Sinclair Ross' "The Lamp at Noon" (dustbowl tragedy)
Sinclair Ross' "The Painted Door"
Richard Conell's "The Most Dangerous Game"