You specified English, but there are some very good translations of many
famous stories.
Gogol's "The Overcoat" is often cited in collections as one of the greatest ever
short stories.
Each chapter of "The Cyberiad: Fables for the Cybernetic Age" by Stanislaw Lem
is self-contained. The translation into English from Polish is considered a
masterly work.
Three Lem stories have appeared (with three Borges stories "Borges and I", "The
Circular Ruins" and "A Sense of Self") in a famous work called:
"The Mind's I: Fantasies and Reflections on Self and Soul", by Douglas Hofstader
and Daniel Dennett.
https://en.wikipedia.org/wiki/The_Mind's_I
(Hofstader wrote "Godel, Escher and Bach". Dennett is a philosopher who has
written extensively on consciousness and the philosophy of mind.)
Harlan Ellison might appeal to you, for example, "I have no mouth, and I must
scream", and "A Boy and his Dog".
I'd also have a look at his anthologies, "Dangerous Visions" and "The Last
Dangerous Visions" for more suggestions (some already made by other posters).
See:
https://en.wikipedia.org/wiki/Dangerous_Visions
https://en.wikipedia.org/wiki/The_Last_Dangerous_Visions#Book_one