Im not an English native so I dont think my answers of Philipe Geubels, Najib Amhali and Ronald Goedemond will mean much but I wonder if theres any good English stand up comedians.
i enjoy Randy Feltface. you can find both of his specials on youtube. its more strong story telling with twists of comedy rather than the usual race/sex/gender jokes
John Mulaney is fantastic as others have said, I also like Mike Birbiglia--he adds a lot of pathos into his act which pays off with great tension-breaking jokes.
"An escalator can never break: it can only become stairs. You should never see an Escalator Temporarily Out Of Order sign, just Escalator Temporarily Stairs. Sorry for the convenience." - Mitch Hedberg