And someone I meant to include but did not (aside from Wells and Verne, who simply seemed so obvious I overlooked putting them on the list):
Olaf Stapledon:
Odd John
Sirius
Last and First Men
Star Maker
And, as he had such an impact on the field (basically ruling it for over a decade), I suppose I should include
John W. Campbell:
The Best of John W. Campbell (especially "Twilight" and "Who Goes There"; though if you get the SF Hall of Fame volumes, these are included in them, as well)
As to
"Doc" Smith, I heartily agree. He was certainly one of the best for space opera, as
George O. Smith was for good old "nuts-and-bolts" sf. For a good example of George O., try
The Complete Venus Equilateral.
Actually, for a good overview of some of the best writers from the Golden Age, there was an entire run of "Best of" volumes, from
Stanley G. Weinbaum, who was one of the first greats of American magazine sf, to
Raymond Z. Gallun,
Fredric Brown (whom I highly recommend; very wonky view of the world, but very, very good),
Fred Pohl,
C. L. Moore,
Henry Kuttner,
Leigh Bracket (who co-wrote the script for
The Empire Strikes Back, by the way, but didn't live to see the finished product). And
Judith Merrill's annual Best of sf anthologies from the 50s and 60s present the changeover from classic Golden Age to New Wave rather well, if somewhat idiosyncratically. And we mustn't leave out
Philip Jose Farmer, who certainly challenged the boundaries with
Strange Relations,
The Lovers,
The Green Odyssey, "Please Don't Wash the Carats", "Riders of the Purple Wage" (included in
Dangerous Visions), etc.
Also
Walter M. Miller Jr's.
A Canticle for Leibowitz, which even someone who has serious reservations about religion can recommend as a thoroughly thought-provoking and just beautifully written book. Though not absolutely essential, I've got to admit I have a high regard for some of
Gordon R. Dickson's work, especially his Childe Cycle (Dorsai series) and I rather like
Time Storm as well.
And for a very different sort of sf (and if you can find a copy) try
David R. Bunch's collection,
Moderan.
Well, now you folks have done it: nearly all my sf is in storage, and now I want to go get it out... AAAAARRRRRGH!