While not precisely classics, we can't leave out Lois McMaster Bujold. If you have been deprived, I'd say start with Cordelia: Shards of Honor and Barrayar.
I had a terrible crush on Poul Anderson's Captain Sir Dominic Flandry as a teenager.
Consuela has mentioned some great books. Mission of Gravity is often cited as one of the best books from an alien point of view. I must differ on The Mote in God's Eye, because of the supposedly brilliant female scientists who turns into a screaming idiot. Jerry Pournelle is in the running for "Most Sexist Author."
Did he ever write a Gor book?
RA Lafferty short stories. He was a huge influence on Neil Gaiman and was a fantastic writer who is also great fun to read.
900 Grandmothers
is one of my favorite books, which I would definitely recommend you buy, except that I see it's scarily expensive on Amazon.
John Norman goes beyond sexism to some more disgusting category.
I hung out with R.A. Lafferty at a couple of World Cons. He was a funny man.
Does anybody really like reading Asimov?
Yes. I have read pretty much the entirety of the Foundation, Robots, and Empire series' (which all end up connecting, in the end) and though I don't necessarily think they are entirely wonderful, I certainly enjoyed them pretty much all the way through. I've read each of the short story collections I have by him at least 5 times each.
I find him to be extraordinarily readable and generally full of pretty fascinating ideas. And I think his work in short stories is often nothing short of amazing, with "The Bicentennial Man" and "The Ugly Little Boy" standing out particularly, though there are plenty of other wonderful examples.
I don't read for word choice or poetic phrasing most of the time, and in fact often find it distracting. Asimov gives good story, at least by my reckoning.
For Anderson "The Merman's
Children" Anderson at his best.
L Sprague de Camp's "Lest darkness fall". Main character kind of a dick, but still very entertaining. Oh and more famous the whole series he wrote (with Fletcher Pratt) about a psycniatrist who ends up in a series of adventure in alternate worlds, and becomes a damn good magician (in multiple senses of the word "good")
Are we not supposed to enjoy Asimov? That's a bunch of poo. I like reading him, sure. Tickles the thinky mathy parts of my brain.
Are we not supposed to enjoy Asimov?
I was just asking if people did. And some people do.
Gleaned from the comments of Mark Reads:
You can pull up Google Maps and ask for the Walking directions from "The Shire" to "Mordor."
You get a special warning.
