Individual short stories often just disappear. Those that remain usually do so for two reasons:
(1) They get anthologized in text books and thus taught in classrooms
(2 They get discussed in articles and books
I have chosen the following list of approximately 200 stories based on those two criteria. I will post a list of stories from the last half of the 20th century next week. The dates reflect when the stories first appeared in book form. If you find errors or omissions, please let me know. I would appreciate it.
1900-1910
Cather, Willa "Paul's Case" 1905
"Sculptor's
Funeral" 1905
Forster, E. M. "Other
Side of the Hedge" 1904
"Road
from Colonus" 1904
"Celestial
Omnibus" 1911
Galsworthy, John "Japanese Quince" 1910
Mann, Thomas "Gladius Dei" 1902
"Infant
Prodigy" 1903
"Tonio
Kroger" 1903
"Death
in Venice" 1912
"Railway
Accident"
"Little
Herr Friedman" 1903
Unamuno, Miguel de "Madness of Dr. Montarco" 1904
1910-1920
Akutagawa, Ryunosuke "Rashomon"
1915
Anderson, Sherwood Winesburg, Ohio 1919
Bunin, Ivan "Gentleman
from San Francisco" 1915
Dreiser, Theodore "Lost Phoebe" 1916
Hesse, Hermann "The
Poet" 1913
Joyce, James Dubliners
1914
Kafka, Franz "Metamorphosis" 1915
"Judgment"
1916
"Country
Doctor" 1919
Lawrence, D. H. "Odor of Chrysanthemums" 1911
"Prussian
Officer" 1913
"White
Stockings" 1914
"Tickets,
Please" 1919
Mansfield, Katherine "Bliss" 1918
Pirandello, Luigi "War" 1919
1920-1930
Akutagawa, Ryunosuke "In
a Grove" 1922
Anderson, Sherwood "The Egg" 1921
"I
Want to Know Why" 1921
"I'm
a Fool" 1922
"Man
Who Became a Woman" 1923
"Death
in the Woods" 1926
Babel, Isaac "How
it Was Done in Odessa" 1923
"Crossing
into Poland" 1924
"My
First Goose" 1924
"Story
of My Dovecote"
Callaghan, Morley "Faithful Wife" 1929
Capek, Karel "Last Judgment" 1929
Connell, Richard "Most Dangerous Game" 1924
Coppard, A.E. "Adam and Eve and Pinch Me"
1921
"Arabesque--the
Mouse" 1921
"The
Higgler" 1924
"Field
of Mustard" 1926
Fitzgerald, F. Scott "Diamond Big as the Ritz" 1922
"Absolution
1925
"The
Rich Boy" 1926
"Winter
Dreams" 1926
Glaspel, Susan "Jury of Her Peers" 1927
Hemingway, Ernest "Indian Camp" 1924
"Big,
Two-Hearted River" 1925
"Soldier's
Home" 1925
"Hills
Like White Elephants" 1927
"In
Another Country" 1927
"The
Killers" 1927
Hurston, Zora Neale "Spunk" 1925
"Sweat"
1926
Huxley, Aldous "Young Archimedes" 1924
Kafka, Franz "Hunger Artist" 1922
Kawabata, Yasunari "Grasshopper and Cricket" 1924
Lagerkvist, Par "Father and I" 1923
Lardner,Ring "Haircut" 1925
"Golden
Honeymoon" 1922
Lawrence, D. H. "Blind Man" 1922
"Horse-Dealer's
Daughter" 1922
"Woman
who Rode Away" 1925
"Rocking-Horse
Winner" 1926
"The
Man Who Loved Islands" 1927
"Two
Blue Birds" 1927
Mann, Thomas "Disorder and
Early Sorrow" 1926
Mansfield, Katherine "Miss Brill" 1920
"Daughters
of the Late Colonel" 1921
"Her
First Ball" 1921
"The
Fly" 1922
"Garden
Party" 1922
"Marriage
a al Mode" 1922
Maughm, Somerset "Rain" 1921
"Outstation"
1924
Parker, Dorothy "Big Blonde" 1929
Porter, Katherine Anne "Maria Concepcion"
1922
"Theft"
1929
Quirgo, Horacio "Dead Man" 1920
Steele, Wilbur Daniel "Footfalls" 1920
Svevo, Italo "Generous Wine" 1927
Toomer, Jean "Fern" 1922
"Blood-Burning
Moon" 1923
"Theater"
1923
Woolf, Virginia "Haunted House" 1921
1930-1940
Aiken, Conrad "Silent
Snow, Secret Snow" 1932
Babel, Isaac "In the
Basement" 1930
"Guy
de Maupassant" 1932
"Di
Grasso" 1937
Beckett, Samuel "Dante and the Lobster" 1932
Bontemps, Arna "Summer Tragedy" 1933
Borges, Jorge Luis "Pierre Menard, Author of Quixote"
1939
Bowen, Elizabeth "Her Table Spread" 1930
"Tears,
Idle Tears" 1937
Boyle, Kay "Astronomer's
Wife" 1936
"White
Horses of Vienna"
Caldwell, Erskin "Kneel to the Rising Sun" 1935
Callaghan, Morley "Sick Call" 1932
Dinesen, Isak "The Monkey" 1934
Faulkner, William "Rose for Emily" 1930
"Dry
September" 1930
"Spotted
Horses" 1931
"That
Evening Sun" 1931
"Barn
Burning" 1939
Gordon, Carol ine "Old
Red" 1933
Greene, Graham "The Basement Room" 1935
Hemingway, Ernest "Clean, Well-Lighted Place" 1933
"Short
Happy Life of Frances Macomber" 1936
Hughes, Langston "On the Road" 1935
Lagerkvist, Par "Children's Campaign" 1935
Landolfi, Tommaso "Wedding Night" 1939
McCarthy, Mary "Cruel and Barbarous Treatment"
1939
O'Connor, Frank "Guests of the Nation" 1930
"First
Confession" 1939
Porter, Katherine Anne" The
Grave" 1935
"Noon
Wine" 1936
"Jilting
of Granny Weatherall" 1930
"Flowering
Judas" 1930
Pritchett, V.S. "Sense of Humor" 1937
Saroyan, William "Daring Young Man on the Flying
Trapeze" 1934
Sartre, Jean Paul "The Wall" 1937
Schorer, Mark "Boy
in the Summer Sun" 1937
Schultz, Bruno "Street of Crocodiles" 1934
Schwartz, Delmore "In Dreams Begin Responsibilities"
1937
Shaw, Irwin "Girls in their Summer
Dresses" 1939
Steele, Wilburn Daniel" How
Beautiful with Shoes" 1932
Steinbeck, John "The Snake" 1936
"Chrysanthemums"
1938
"Flight"
1938
Unamuno Miguel "St. Emmanuel the Good, Martyr"
1933
Welty, Eudora "Death of a Traveling
Salesman" 1936
"A
Piece of News" 1937
"Petrified
Man" 1939
Williams, William Carlos"
Use of Force" 1938
Wolfe, Thomas "Only the
Dead Know Brooklyn" 1939
Fitzgerald, F. Scott "Babylon Revisited" 1930
Wright, Richard "Big Boy Leaves Home" 1936
"Bright
and Morning Star" 1937
1940-1950
Borges, Jorge Luis "Circular Ruins" 1940
"Tlon,
Ugbar, Orbis, Tertius" 1940
"Garden
of Forking Paths" 1941
"Lottery
in Babylon" 1941
"Library
of Babel" 1941
"Funes
the Memorious" 1944
Bowen, Elizabeth "Demon Lover" 1940
"Happy
Autumn Fields" 1944
"Queer
Heart" 1941
Bowles, Paul "The Scorpion" 1945
"Distant
Episode" 1947
Capote, Truman "Tree of Night" 1943
"Miriam"
1945
Cheever, John "Enormous Radio" 1947
Clarke, Walter van Tilburg "Portable
Phonograph" 1941
"The
Wind and the Snow of Winter" 1944
Dinesen, Isak "Sailor-Boy's Tale" 1942
"Sorrow
Acre" 1942
"Blue
Jar" 1922
Ellison, Ralph "King of the Bingo Game" 1944
"Flying
Home" 1944
Gordimer, Nadine "Train from Rhodesia" 1947
Greene, Graham "Across the Bridge" 1949
"Hint
of an Explanation" 1949
Jackson, Shirley "The Lottery" 1948
Lavin, Mary "A Wet Day" 1944
"The
Will" 1944
McCullers, Carson "Tree, Rock, Cloud" 1942
Nabokov, Vladimir "That in Aleppo Once" 1943
"Signs
and Symbols" 1948
O'Connor, Frank "Judas" 1947
"Drunkard"
1948
O'Faolain, Sean "Man Who Invented Sin" 1944
"Innocence"
1946
O'Flaherty, Liam "Two Lovely Beasts" 1946
Powers, J. F. "Lions, Harts, and Leaping
Does" 1943
"Prince
of Darkness" 1946
"The
Forks" 1947
"Valiant
Woman" 1947
Pritchett, V.S. "Saint" 1940
Salinger, J. D. "Perfect Day for Bananafish"
1948
"Uncle
Wiggly in Connecticut" 1948
Saroyan,William "Summer of Beautiful White
Horse" 1940
Shaw, Irwin "Act of
Faith" 1946
Singer, I.B. "Spinoza of Market Street"
1944
"Gimpel
the Fool" 1957
Stafford, Jean "Interior Castle" 1947
Stegner, Wallace "Butcher Bird" 1940
Taylor, Peter "Fancy Woman" 1940
Trilling, Lionel "Of This Time, Of That Place"
1943
Warren, Robert Penn"Blackberry
Winter" 1946
Welty, Eudora "Keela,
the Outcast Indian Maiden" 1940
"A
Visit of Charity" 1941
"Why
I Live at the PO" 1941
"Worn
Path" 1941
"Powerhouse"
1941
White, E. B. "Second Tree from the
Corner" 1947
Wright, Richard "Man
Who Was Almost a Man" 1940