:smack:
That’s Joss Whedon, you heretic! 
To add to the author list: Eric Flint has a great series going. Start with 1632 and go from there.
I’m also a fervent Tuf fan. The book came out in 1987 and is indeed out of print now, but copies are pretty easily found online. I read it again every three or four years - outstanding SF, with a great central character, funny dialogue and intriguing ideas. I’ve always thought it would make a great movie. Martin told me a few years ago that he hopes to write a Tuf sequel once his massive “A Song of Fire and Ice” swords-and-sorcery double trilogy is complete.
The Dancers at the End of Time by Michael Moorcock would be good. (As others have mentioned they do with their favourites, I re-read this once in a while.)
The best of all, IMHO, is Cordwainer Smith. I always recommend him in threads like this, and haven’t heard of anybody who disagrees. (If they’re out there, they’re wrong, so ignore them. 
)
Alfred Bester. The Stars My Destination is the definitive space opera. The Demolished Man put him on the map, but IMHO isn’t as good as Stars.
Actually, you could make a case that Bester represents the bridge between the classic writers and the New Wave…
By the way, you say in the OP that Asimov and Heinlein don’t do much for you… Would you mind saying which Heinleins you’ve read? There’s a lot of variability in his stuff. If you started on Stranger in a Strange Land, don’t take that as representative. Some people love it, but some people hate it. Either way, it’s quite possible to like his other works.
If, on the other hand, you’ve read, say, The Moon is a Harsh Mistress and didn’t like it, then it’s probably safe to say that Heinlein just isn’t the author for you.
I might have missed if it was suggested before, but Neuromancer by William Gibson is an excellent science-fiction book. Also, the Stainless Steel Rat series by Harry Harrison are nice little bites of sci-fi.
Oh man, is this the one where they launched all the forests into space? And it had three or four cute little robot guys? I saw that movie when I was quite young and I have been trying to recall the title for ages.
Read Robert A. Heinlein.
Start with his juveniles, which are better than most current novels by many other authors.
Try S. Andrew Swann.
Oh yeah, Zenna Henderson. Try her, too.
Yep - Huey, Dewey, and Louie.
They were not robots or machines of any kind. There’s real people inside.
As mentioned, it does get a bit preachy, but it is pretty good, albeit sad.
Man, somebody beat me to The Stars My Destination. Yeah, it’s “older”, but trust me, it’s amazingly good. And personally I don’t really care for some of the “giants” of the field either - I can appreciate their influences but that doesn’t mean their books stand up. Also Cordwainer Smith, although that’s also quite old - it’s amazingly fresh.
Since I was beaten to my first two picks, how about A Canticle for Leibowitz? It’s really three post-apocalyptic stories about human nature, the preservation of knowledge, etc. It’s really, really good - I finished it sort of stunned.
How about Connie Willis? The first intentionally funny book to win the Hugo is To Say Nothing of the Dog, a time travel book. It’s very funny, particularly if you’ve read things like Three Men in a Boat. She also wrote The Doomsday Book, which is also a time travel book but is very, very sad. Both are excellent.
Star Trek!
Surprisingly I don’t think anyone’s mentioned him so far, but David Brin has probably been the biggest SF author in the last twenty years. Read pretty much anything of his.
The essential Robert Heinlein (in no particular order):
**Double Star
The Moon is a Harsh Mistress
The Puppet Masters
Tunnel in the Sky
Citizen of the Galaxy
The Door into Summer
Starman Jones
Have Space Suit - Will Travel
Starship Troopers (not at ALL like the movie)
The Rolling Stones
Time for the Stars
The Star Beast
**
The more controversial Heinlein books:
**
Stranger in a Strange Land
Time Enough for Love
To Sail Beyond the Sunset
Friday
I Will Fear No Evil
The Number of the Beast
**
Plus there are other works. I would highly recommend anything off the first list. If I had to pick just one for someone who had never read Heinlein, I’d probably recommend “Citizen of the Galaxy”, “The Door Into Summer”, or “Double Star”. But all from that first list are fantastic. They’ve all become classics.
The second bunch are either fairly political, or have controversial content (incest, etc), or are just plain poorly written (“I Will Fear no Evil”). Heinlein was an old, ailing man when he wrote some of those. But the earlier stuff (say, anything written before 1965) is tremendous.
Also highly recommended is his short story collection. You can find almost all of them in a two volume collection called The Past Through Tomorrow.
Arthur C. Clarke: Songs of Distant Earth.
Hm, I don’t know if I’d call TSMD a space opera. Gully Foyle is way more debased than the average hero of a space opera, and the characterization is much more deep than that in a typical SO. I’d call this proto-New Wave or even proto-proto-cyberpunk (compare the relationship of the characters to technology in this and a typical cyberpunk novel–it’s basically the same, a relationship that is advantageous to those working around the system but detrimental to those people staying in it).
Most of what I read falls into either the New Wave or (post-)cyberpunk subgenres. There are only a handful of Golden Age writers I like–Bester and Clifford Simak are the only two that really come to mind, and you could make a case for both of them being anomalies that might be better described as New Wave writers.
I’d recommend anything by Philip K. Dick, but especially Martian Time-Slip, Do Androids Dream of Electric Sheep?, Radio Free Albemuth (trippy, but awesome–and if you like dystopias you’ll love this), A Scanner Darkly, and the Valis trilogy (though I’d hold off on reading this until you’ve read a lot more of his work). PKD is my favorite writer, I love his stuff like some people love Heinlein. Actually, if you don’t like Heinlein I’d recommend checking out Dick because most of the Dick fanatics I know hate Heinlein. I don’t know why that is, but it seems to be a general rule. I don’t know if Heinlein super-fans hate PKD.
Some other good New Wave writers: Harlan Ellison (short stories, also check out Dangerous Visions even though he just edited it), Stanislaw Lem (Solaris. The Futurological Congress), and John Brunner (just avoid later stuff, ick). Ursula K. LeGuin’s novel The Lathe of Heaven is wonderful but I can’t get into anything else by her. I don’t know if Kurt Vonnegut counts as New Wave (according to him, he never wrote a word of science fiction), but definitely check out Player Piano, The Sirens of Titan, Cat’s Cradle… oh hell, just read everything, same as you should with Dick.
Some good cyberpunk or post-cyberpunk writers/books: William Gibson (I honestly didn’t like any of the Sprawl books–the series that includes Neuromancer–as much as I did the bridge trilogy, which starts out with Virtual Light), Neal Stephenson (but ONLY Snow Crash–everything else is bloated and self-referential), Cory Doctorow (a new writer–Down and Out in the Magic Kingdom is a great introduction to post-cyberpunk), Gun, with Occasional Music by Jonathan Lethem, and Hard-Boiled Wonderland and the End of the World by Haruki Murakami (heavy and sorta literary, but I loved it).
If you like dystopias, I’ll recommend Beautiful Soup by Harvey Jacobs, The Handmaid’s Tale by Margaret Atwood, A Canticle for Leibowitz by Walter M. Miller, and of course the classic Brave New World by Aldous Huxley.
I read no hard SF at all, so I can’t help you there. I would like to suggest using your library to check books out, so you don’t have to worry about spending money on something you won’t like. I know that most of PKD’s books are available at the library, for instance.