The very first annual best-of-the-year anthology series began in 1949, edited by Everett F. Bleiler (
SFE) and T.E. Dikty (
SFE), the former best known as a bibliographer, the latter as an editor and publisher. Published in hardcover, the series had an irregular run: annual volumes of "Best Science Fiction Stories" from 1949 through 1954, a companion set of "Year's Best Science Fiction Novels" from 1952 to 1954, and then -- under Dikty's editorship alone -- combined volumes of "Best Science Fiction Stories and Novels" for 1955, 1956, and after a year's absence, a "Ninth Series" published in 1958; the last two of these volumes were much slimmer than earlier anthologies, and included stories from each of the previous two years.
The photo below shows 9 of the total 12 anthologies.
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The Best Science-Fiction Stories: 1949, (Frederick Fell, 1949)
(isfdb)
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The Best Science-Fiction Stories: 1950, (Frederick Fell, 1950)
(isfdb)
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The Best Science-Fiction Stories: 1951, (Frederick Fell, 1951)
(isfdb)
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The Best Science-Fiction Stories: 1952, (Frederick Fell, 1952)
(isfdb)
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Year's Best Science Fiction Novels: 1952, (Frederick Fell, 1952)
(isfdb)
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The Best Science-Fiction Stories: 1953, (Frederick Fell, 1953)
(isfdb)
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Year's Best Science Fiction Novels: 1953, (Frederick Fell, 1953)
(isfdb)
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The Best Science-Fiction Stories: 1954, (Frederick Fell, 1954)
(isfdb)
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Year's Best Science Fiction Novels: 1954, (Frederick Fell, 1954)
(isfdb)
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The Best Science-Fiction Stories and Novels: 1955, (Frederick Fell, 1955)
(isfdb)
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The Best Science Fiction Stories and Novels: 1956, (Frederick Fell, 1956)
(isfdb)
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The Best Science Fiction Stories and Novels: 9th Series, (Advent:Publishers, 1958)
(isfdb)
Complete Contents by Author and Title
Poul Anderson
Flight to Forever
(1950)
-- Year's Best Science Fiction Novels: 1952
Genius
(1948)
-- The Best Science-Fiction Stories: 1949
Trespass!
(by PA & Gordon R. Dickson)
(1950)
-- The Best Science-Fiction Stories: 1951
Alex Apostolides
What Thin Partitions
(by Mark Clifton & AA)
(1953)
-- The Best Science-Fiction Stories: 1954
Isaac Asimov
No Connection
(1948)
-- The Best Science-Fiction Stories: 1949
Alfred Bester
Oddy and Id
(1950)
-- The Best Science-Fiction Stories: 1951
Of Time and Third Avenue
(1951)
-- The Best Science-Fiction Stories: 1952
Time Is the Traitor
(1953)
-- The Best Science-Fiction Stories: 1954
James Blish
Surface Tension
(1952)
-- Year's Best Science Fiction Novels: 1953
Anthony Boucher
Nine-Finger Jack
(1951)
-- The Best Science-Fiction Stories: 1952
Ray Bradbury
...And the Moon Be Still as Bright
(1948)
-- The Best Science-Fiction Stories: 1949
Dwellers in Silence
(1948)
-- The Best Science-Fiction Stories: 1950
The Fox in the Forest
(1950)
-- The Best Science-Fiction Stories: 1951
The Man
(1949)
-- The Best Science-Fiction Stories: 1950
Mars Is Heaven!
(1948)
-- The Best Science-Fiction Stories: 1949
The Pedestrian
(1951)
-- The Best Science-Fiction Stories: 1952
Reginald Bretnor
The Gnurrs Come from the Voodvork Out
(1950)
-- The Best Science-Fiction Stories: 1951
Bill Brown
The Star Ducks
(1950)
-- The Best Science-Fiction Stories: 1951
Fredric Brown
Dark Interlude
(by FB & Mack Reynolds)
(1951)
-- The Best Science-Fiction Stories: 1952
Knock
(1948)
-- The Best Science-Fiction Stories: 1949
The Last Martian
(1950)
-- The Best Science-Fiction Stories: 1951
Mouse
(1949)
-- The Best Science-Fiction Stories: 1950
Robert Spencer Carr
Easter Eggs
(1949)
-- The Best Science-Fiction Stories: 1950
John Christopher
Balance
(1951)
-- The Best Science-Fiction Stories: 1952
Arthur C. Clarke
Seeker of the Sphinx
(1951)
-- Year's Best Science Fiction Novels: 1952
Mark Clifton
The Conqueror
(1952)
-- The Best Science-Fiction Stories: 1953
What Thin Partitions
(by MC & Alex Apostolides)
(1953)
-- The Best Science-Fiction Stories: 1954
Alfred Coppel
The Dreamer
(1952)
-- The Best Science-Fiction Stories: 1953
J. J. Coupling
Period Piece
(1948)
-- The Best Science-Fiction Stories: 1949
Kendell Foster Crossen
Assignment in Aldebaran
(1953)
-- Year's Best Science Fiction Novels: 1954
Betsy Curtis
A Peculiar People
(1951)
-- The Best Science-Fiction Stories: 1952
Max Dancey
The Collectors
(by G. Gordon Dewey & MD)
(1953)
-- The Best Science-Fiction Stories: 1954
L. Sprague de Camp
Summer Wear
(1950)
-- The Best Science-Fiction Stories: 1951
G. Gordon Dewey
The Collectors
(by GGD & Max Dancey)
(1953)
-- The Best Science-Fiction Stories: 1954
Philip K. Dick
Second Variety
(1953)
-- Year's Best Science Fiction Novels: 1954
Gordon R. Dickson
Trespass!
(by Poul Anderson & GRD)
(1950)
-- The Best Science-Fiction Stories: 1951
Boyd Ellanby
Category Phoenix
(1952)
-- Year's Best Science Fiction Novels: 1953
Erik Fennel
Doughnut Jockey
(1948)
-- The Best Science-Fiction Stories: 1949
Martin Gardner
Thang
(1948)
-- The Best Science-Fiction Stories: 1949
H. L. Gold
The Enormous Room
(by HLG & Robert W. Krepps)
(1953)
-- Year's Best Science Fiction Novels: 1954
Ruth M. Goldsmith
Yankee Exodus
(1953)
-- The Best Science-Fiction Stories: 1954
David Grinnell
Extending the Holdings
(1951)
-- The Best Science-Fiction Stories: 1952
Charles L. Harness
The New Reality
(1950)
-- The Best Science-Fiction Stories: 1951
Zenna Henderson
Ararat
(1952)
-- The Best Science-Fiction Stories: 1953
John Jakes
Machine
(1952)
-- The Best Science-Fiction Stories: 1953
Will F. Jenkins
Doomsday Deferred
(1949)
-- The Best Science-Fiction Stories: 1950
Damon Knight
To Serve Man
(1950)
-- The Best Science-Fiction Stories: 1951
C. M. Kornbluth
The Marching Morons
(1951)
-- The Best Science-Fiction Stories: 1952
The Mindworm
(1950)
-- The Best Science-Fiction Stories: 1951
Robert W. Krepps
The Enormous Room
(by H. L. Gold & RWK)
(1953)
-- Year's Best Science Fiction Novels: 1954
Five Years in the Marmalade
(1949)
-- The Best Science-Fiction Stories: 1950
Walter Kubilius
The Other Side
(1951)
-- The Best Science-Fiction Stories: 1952
Henry Kuttner
Happy Ending
(1948)
-- The Best Science-Fiction Stories: 1949
Private Eye
(1949)
-- The Best Science-Fiction Stories: 1950
Fritz Leiber
Appointment in Tomorrow
(1951)
-- The Best Science-Fiction Stories: 1952
A Bad Day for Sales
(1953)
-- The Best Science-Fiction Stories: 1954
The Big Holiday
(1953)
-- The Best Science-Fiction Stories: 1954
Coming Attraction
(1950)
-- The Best Science-Fiction Stories: 1951
The Moon Is Green
(1952)
-- The Best Science-Fiction Stories: 1953
Murray Leinster
The Gadget Had a Ghost
(1952)
-- Year's Best Science Fiction Novels: 1953
The Life-Work of Professor Muntz
(1949)
-- The Best Science-Fiction Stories: 1950
The Middle of the Week After Next
(1952)
-- The Best Science-Fiction Stories: 1953
The Sentimentalists
(1953)
-- Year's Best Science Fiction Novels: 1954
The Strange Case of John Kingman
(1948)
-- The Best Science-Fiction Stories: 1949
Frank Belknap Long
Two Face
(1950)
-- The Best Science-Fiction Stories: 1951
John D. MacDonald
Flaw
(1949)
-- The Best Science-Fiction Stories: 1950
Game for Blondes
(1952)
-- The Best Science-Fiction Stories: 1953
Katherine MacLean
Contagion
(1950)
-- The Best Science-Fiction Stories: 1951
Richard Matheson
Born of Man and Woman
(1950)
-- The Best Science-Fiction Stories: 1951
The Last Day
(1953)
-- The Best Science-Fiction Stories: 1954
Lover, When You're Near Me
(1952)
-- The Best Science-Fiction Stories: 1953
Witch War
(1951)
-- The Best Science-Fiction Stories: 1952
J. T. McIntosh
One in Three Hundred
(1953)
-- The Best Science-Fiction Stories: 1954
Walter M. Miller, Jr.
Command Performance
(1952)
-- The Best Science-Fiction Stories: 1953
Conditionally Human
(1952)
-- Year's Best Science Fiction Novels: 1953
Crucifixus Etiam
(1953)
-- The Best Science-Fiction Stories: 1954
Izzard and the Membrane
(1951)
-- Year's Best Science Fiction Novels: 1952
Ward Moore
Lot
(1953)
-- The Best Science-Fiction Stories: 1954
William Morrison
The Model of a Judge
(1953)
-- The Best Science-Fiction Stories: 1954
Lewis Padgett
Ex Machina
(1948)
-- The Best Science-Fiction Stories: 1949
Peter Phillips
At No Extra Cost
(1951)
-- The Best Science-Fiction Stories: 1952
Arthur Porges
The Fly
(1952)
-- The Best Science-Fiction Stories: 1953
The Rats
(1951)
-- The Best Science-Fiction Stories: 1952
Mack Reynolds
Dark Interlude
(by Fredric Brown & MR)
(1951)
-- The Best Science-Fiction Stories: 1952
Frank M. Robinson
The Girls from Earth
(1952)
-- The Best Science-Fiction Stories: 1953
The Hunting Season
(1951)
-- Year's Best Science Fiction Novels: 1952
The Oceans Are Wide
(1954)
-- Year's Best Science Fiction Novels: 1954
Eric Frank Russell
...And Then There Were None
(1951)
-- Year's Best Science Fiction Novels: 1952
Fast Falls the Eventide
(1952)
-- The Best Science-Fiction Stories: 1953
I Am Nothing
(1952)
-- The Best Science-Fiction Stories: 1953
Idris Seabright
Brightness Falls from the Air
(1951)
-- The Best Science-Fiction Stories: 1952
Joseph Shallit
Wonder Child
(1953)
-- The Best Science-Fiction Stories: 1954
Wilmar H. Shiras
In Hiding
(1948)
-- The Best Science-Fiction Stories: 1949
Opening Doors
(1949)
-- The Best Science-Fiction Stories: 1950
Clifford D. Simak
Eternity Lost
(1949)
-- The Best Science-Fiction Stories: 1950
Theodore Sturgeon
The Hurkle Is a Happy Beast
(1949)
-- The Best Science-Fiction Stories: 1950
William F. Temple
Counter-Transference
(1952)
-- The Best Science-Fiction Stories: 1953
Forget-Me-Not
(1950)
-- The Best Science-Fiction Stories: 1951
The Two Shadows
(1951)
-- The Best Science-Fiction Stories: 1952
William Tenn
Firewater
(1952)
-- Year's Best Science Fiction Novels: 1953
Generation of Noah
(1951)
-- The Best Science-Fiction Stories: 1952
Wilson Tucker
The Tourist Trade
(1951)
-- The Best Science-Fiction Stories: 1952
A. E. van Vogt
Process
(1950)
-- The Best Science-Fiction Stories: 1951
Jack Vance
DP!
(1953)
-- The Best Science-Fiction Stories: 1954
Men of the Ten Books
(1951)
-- The Best Science-Fiction Stories: 1952
Robert Moore Williams
Refuge for Tonight
(1949)
-- The Best Science-Fiction Stories: 1950
John Wyndham
Survival
(1952)
-- The Best Science-Fiction Stories: 1953
Roger Flint Young
Not to Be Opened
(1950)
-- The Best Science-Fiction Stories: 1951