Some of the very best sci-fi anthologies ever published
Before the Golden Age edited by Isaac Asimov (1974)
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One suspects that BGA's enduring popularity has more to do with Asimov's insightful and often humourous biographical anecdotes, rather than the stories found within. The master escorts us through stories from the 1930s that he asserts, "have a rough-hewn vigor about them that sophistication has, to some extent, lost us."
The Road to Science Fiction edited by James Gunn (1977-82)
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Sci-fi's mid-70s elevation to academic credibility saw the publication of several all-encompassing 'historical anthologies' - which often-times bit off more than they could chew. Atypically, the stories in the first four volumes of the Road series are well-selected & insightfully annotated - with Gunn capably spreading his critical wings in #4.
Science Fiction Hall of Fame eds Silverberg & Bova (1970/73)
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Members of the Science Fiction Writers of America were polled on what they thought represented the best sci-fi short fiction written before the first Nebula awards were handed out in 1966. Not surprisingly, the result is probably as close as we'll ever get to a definitive collection of early science fiction, as evidenced by the fact they are still in print.
The Hugo Winners edited by Asimov, et al (1962-97)
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The Hugo and Nebula awards kicked off in 1953 and 1966 respectively - with Isaac Asimov being the first to anthologise a collection of award-winning stories in the early-60s. Asimov lent both his name and laconic wit to the well-organised New Hugo Winners series, which suffered an unannounced and premature termination in 1997.
The Best of the Nebulas edited by Ben Bova (1989)
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Bova puts his involvement in the earliest incarnations of award-winner anthologies to good use in this top-notch collection of Nebula luminaries. Spanning a quarter-century, the stories fill almost 600 pages with barely a wasted word. Perhaps the only notable all-encompassing single volume that achieves what it sets out to do.
Dangerous Visions edited by Harlan Ellison (1967 & 1972)
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The declining popularity of pulpish genre magazines in the mid-60s gave rise to a wave of 'original anthologies' of first-time published short story collections. DV was an attempt at collecting together a single volume of cutting edge stories that no-one else would publish. The less-famous Again follow-up was closer to the mark, however both are worthwhile.
Future on Fire (& Ice) edited by Orson Scott Card (1991/98)
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Distinctively Eighties anthology showcasing "the decade's hottest writers" - including William Gibson, Kim Stanley Robinson, Pat Cadigan, Connie Willis and Bruce Sterling. The Future on Ice companion volume appeared seven years later in 1998 - containing most of the top writers that missed out the first time around. Get both for a good 80s overview.
Year's Best Science Fiction ed Gardner Dozois (1984-present)
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Anthologised collections of the year's best short sci-fi have been popular for over three decades. Dozois' on-going annual collections regularly scoop the relevant major awards - with the Sixth and Twelfth in the series being particularly strong. Unfortunately, often somewhat disjointed owing to the need to appeal to the masses.