Here are three books that assemble the best stories that have already won their respective awards.
The 1989 Nebula volume is the result of a vote by SFWA members in 1987, in a process described in Ben Bova's introduction, and which included votes on novels. The book presents 21 novellas, novelettes, and short stories, in approximately chronological order, with forewords by the authors. There are also essays about the top 10 placing novels. Ranking of the results are not given.
The 1992 Hugo volume is the result of a vote at the 50th World Science Fiction Convention to determine the favorite works in all categories of the Hugo Awards, not just the fiction categories. The book presents the top four short stories, top three novelettes, and top three novellas. Complete results and voting statistics for all categories are given at the end. The book is "presented" by Isaac Asimov, who died before the book was finished; though not credited on the cover, Charles Sheffield stepped in to provide a introductions to the book and to each story.
The 2004 Locus volume presents 18 stories that won Locus Awards from 1971 to 2003, as selected by editors Brown and Strahan: "We've gone through the thirty years of winners and picked what we think are the best."
No story appears in all three volumes; five stories, two by Ellison and one each by Le Guin, Martin, and Varley, appear in two volumes. With multiple stories, Harlan Ellison is reprinted 6 times in these three books, George R.R. Martin and James Tiptree, Jr., three times each.
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The Best of the Nebulas, Ben Bova, ed. (Tor, 1989)
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The Super Hugos, Martin H. Greenberg, ed. (Baen, 1992)
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The Locus Awards, Charles N. Brown & Jonathan Strahan, eds. (Eos, 2004)
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Combined Contents by Author and Title
Isaac Asimov
The Bicentennial Man
(Stellar, 1976)
-- The Super Hugos
Terry Bisson
Bears Discover Fire
(IASFM Aug 1990)
-- The Locus Awards
Octavia E. Butler
Bloodchild
(IASFM Jun 1984)
-- The Locus Awards
Ted Chiang
Hell Is the Absence of God
(Starlight 3, 2001)
-- The Locus Awards
Arthur C. Clarke
The Star
(Infinity Science Fiction Nov 1955)
-- The Super Hugos
John Crowley
Gone
(F&SF Sep 1996)
-- The Locus Awards
Samuel R. Delany
Aye, and Gomorrah...
(Dangerous Visions, 1967)
-- The Best of the Nebulas
Time Considered as a Helix of Semi-Precious Stones
(New Worlds Dec 1968)
-- The Best of the Nebulas
Greg Egan
Border Guards
(Interzone Oct 1999)
-- The Locus Awards
Harlan Ellison
A Boy and His Dog
(New Worlds Apr 1969)
-- The Best of the Nebulas
I Have No Mouth, and I Must Scream
(If Mar 1967)
-- The Super Hugos
Jeffty Is Five
(F&SF Jul 1977)
-- The Best of the Nebulas
-- The Locus Awards
'Repent, Harlequin!' said the Ticktockman
(Galaxy Dec 1965)
-- The Best of the Nebulas
-- The Super Hugos
Neil Gaiman
October in the Chair
(Conjunctions #39 2002)
-- The Locus Awards
John Kessel
Buffalo
(F&SF Jan 1991)
-- The Locus Awards
Daniel Keyes
Flowers for Algernon
(F&SF Apr 1959)
-- The Super Hugos
Ursula K. Le Guin
The Day Before the Revolution
(Galaxy Aug 1974)
-- The Best of the Nebulas
-- The Locus Awards
Fritz Leiber
Catch That Zeppelin!
(F&SF Mar 1975)
-- The Best of the Nebulas
Gonna Roll the Bones
(Dangerous Visions, 1967)
-- The Best of the Nebulas
Barry B. Longyear
Enemy Mine
(IASFM Sep 1979)
-- The Super Hugos
George R. R. Martin
Sandkings
(Omni Aug 1979)
-- The Best of the Nebulas
-- The Super Hugos
The Way of Cross and Dragon
(Omni Jun 1979)
-- The Locus Awards
Anne McCaffrey
Dragonrider
(Analog Dec 1967 (+1))
-- The Best of the Nebulas
Weyr Search
(Analog Oct 1967)
-- The Super Hugos
Vonda N. McIntyre
Of Mist, and Grass, and Sand
(Analog Oct 1973)
-- The Best of the Nebulas
Michael Moorcock
Behold the Man
(New Worlds #166 1966)
-- The Best of the Nebulas
Pat Murphy
Rachel in Love
(IASFM Apr 1987)
-- The Locus Awards
Larry Niven
Neutron Star
(If Oct 1966)
-- The Super Hugos
Joanna Russ
Souls
(F&SF Jan 1982)
-- The Locus Awards
When It Changed
(Again, Dangerous Visions, 1972)
-- The Best of the Nebulas
Lucius Shepard
The Scalehunter's Beautiful Daughter
(Asimov's Sep 1988)
-- The Locus Awards
Robert Silverberg
Passengers
(Orbit 4, 1968)
-- The Best of the Nebulas
Clifford D. Simak
The Big Front Yard
(Astounding Oct 1958)
-- The Super Hugos
Grotto of the Dancing Deer
(Analog Apr 1980)
-- The Best of the Nebulas
Bruce Sterling
Maneki Neko
(F&SF May 1998)
-- The Locus Awards
Theodore Sturgeon
Slow Sculpture
(Galaxy Feb 1970)
-- The Best of the Nebulas
James Tiptree, Jr.
Houston, Houston, Do You Read?
(Aurora: Beyond Equality, 1976)
-- The Best of the Nebulas
Love Is the Plan the Plan Is Death
(The Alien Condition, 1973)
-- The Best of the Nebulas
The Only Neat Thing to Do
(F&SF Oct 1985)
-- The Locus Awards
John Varley
The Persistence of Vision
(F&SF Mar 1978)
-- The Best of the Nebulas
-- The Locus Awards
Connie Willis
Even the Queen
(IASFM Apr 1992)
-- The Locus Awards
Gene Wolfe
The Death of Doctor Island
(Universe 3, 1973)
-- The Locus Awards
Roger Zelazny
The Doors of His Face, the Lamps of His Mouth
(F&SF Mar 1965)
-- The Best of the Nebulas
He Who Shapes
(Amazing Jan 1965 (+1))
-- The Best of the Nebulas