The short story is a staple in American literature, and it’s fun to read shorter works from time to time.
Edgar Allan Poe influenced Baudelaire, who influenced the rest of French literature, and is worth reading.
For contemporary stories, see T.C. Boyle (editor), Doubletakes: Pairs of Contemporary Short Stories (Cengage Learning, 2003).
For a range of short works, see Alan Ziegler (editor), Short: An International Anthology of Five Centuries of Short- Short Stories, Prose Poems, Brief Essays, and Other Short Prose Forms (Persea, 2014).