My must-must read, something essential, not only classical, what everyone who likes sf must read consists of:
Novels:
Isaac Asimov "Foundation" (only first three classical stories)
Pierre Boulle "Monkey planet"
Ray Bradbury "451 Fahrenheit"
David Brin "Startide Rising"
Arthur C. Clarke "Childhood's End"
Philip K. Dick "Man on the High Castle", "Ubik", "Eye on the Sky"
James Gunn "The Listeners"
Joe Haldeman "Forever War"
Daniel Keyes "Flowers for Algernon"
Sergiej Lukjanienko "Лабиринт отражений", "Фальшивые зеркала" (The Deep series)
Walter M. Miller Jr. "Canticle for Leibovitz"
A. & B. Strugatsky "Monday Begins on Saturday", "Roadside Picnic"
John Wyndham "Day of the Tryfids"
Short stories:
Poul Anderson "Sam Hall"
Karl Michael Armer "It's All Over Now, Baby Blue"
Isaac Asimov "Bicentennial Man"
David Brin "Thor meets Captain America", "Crystal Spheres"
Kir Bulyczow - all stories about Guslar
Arthur C. Clarke - every short story is a masterpiece
Philip K. Dick - almost everything (I love "The pre-persons")
Philip Jose Farmer "Riders of the Purple Wage" from "Dangerous Visions"
Shin'ichi Hoshi "City like a Pastureland" (that title was in polish)
James Patrick Kelly "Monsters"
Bob Leman "The Time of the Worm"
Siergiej Lukjanienko "Поезд в Теплый Край"
George R.R. Martin "Sandkings", "For a Single Yesterday", "The Storms of Windhaven"
Sean McMullen "Colours of the Soul"
Frantisek Novotny "Madonna from the Wreck..." (? czech short story)
Frederik Pohl "The Gold at Starbow's End"
Lester del Rey "Evensong" from "Dangerous Visions"
Robert Sheckley - everything
John T. Sladek "The Happy Breed" from "Dangerous Visions"
Henry Slesar "Ersatz" from "Dangerous Visions"
James Tiptree Jr. "The Screwfly Solution"
A.E. van Vogt - almost everything
Connie Willis "Wind of the Marble Arch"
Timothy Zahn "Pawn's Gambit"
...and many, many more...