The thread for the best SF short story reminded me that I’ve enjoyed a lot of SF over the years. However it can be difficult to find gripping novels and often short story collections are more rewarding.
For me the Science Fiction Hall of Fame Volumes I and II are the finest collection, albeit dated now.
One point - I do not like collections edited by Gardner R. Dozois. Clearly I’m in a minority. 
What do you suggest?
Dangerous Visions for an original anthology.
Single author collections would include John Varley’s The Persistence of Vision, Gene Wolfe’s The Island of Doctor Death and Other Stories and Other Stories, and Tom Reamy’s San Diego Lightfoot Sue
For reprint anthologies, I’d look for anything edited by Groff Conklin.
Yes. Very dated, but the Conklin anthologies are gold mines.
I really like the L. Ron Hubbard Writers of the Future anthologies. While there’s an occasional story that I really just don’t care for, usually the stories are excellent. Just try to ignore the Hubbard name that’s on the books.
The simplest route is any of the various volumes of Hugo winners. You won’t get the Best of All Time unless you read all of them, but hey, having a lot of material is good, when it’s high-quality material.
I agree about The Science Fiction Hall of Fame, volumes I, IIA, and IIB. So NOT get volumes III and IV, which are awful. I came in to this thread to recommend the first two volumes.
If you think those are dated, then my other suggestion is even more dated (although still great) – Adventures in Time and Space edited by Healy and McComas. It waas only available in hardcover (or excerpted in paperback) from 1946 until 1975, when it finally appeared unabridged in paperback. It was reprinted a couple of times after that. A measure of its importance is that several of the stories were turned into films (with changed titles) – The Day the Earth Stood Still, The Thing, The Twonky. Two others have relationships to films – Raymond F. Jones’ Correspondence Course feels like a tryout for what became This Island Earth, and Van Vot’s Black Destroyer was the first monster-on-a-spaceship story, which arguably inspired It! The Terror from Beyond Space and Alien. Sadly, it’s out of print, but I still see it at used bookstores.
If you’re looking for recent SF, I can’t recommend a regular series besides Gardner Dozois’, which you’ve already nixed. There are plenty of other anthologies out there, but no series I’ aware of that can be recommended.
I echo the recommendation of “Adventures in Time and Space.” The Golden Age in one big book.
Another good series, though I haven’t seen any in ages, is the Judith Merrill Best SF from 1956 - 1968, which goes from good traditional sf right into the New Wave in later editions. Of the single magazine collections, I like the Best From F&SF best. Also pretty old.
Nothing wrong with older SF, some of the most enjoyable stories I’ve read were by A E Van Vogt and Stanislaw Lem.
Any collection by Groff Conklin. Also any of the Galaxy Readers edited by HL Gold. The later ones edited by Fred Pohl are also pretty good but not as good as the earlier ones by Gold.
I’ll fourth Groff Conklin. I see his name on an anthology, I know I’m in for some good reading. Not sure why he was so much better than the other editors, but he certainly was.
Here’sone I particularly like… but unfortunately it’s probably very hard to find nowadays.
Another fun one is Before the Golden Age… a collection of 1930s stories.
And I would like to join the chorus of praise for Adventures in Time and Space.
You’ve probably already read it, but “I, Robot” by Asimov is classic.
Here’s a list of Groff Conklin anthologies and their tables of contents.
Out of curiosity, what’s your issue with Dozois collections, OP?