Anything by Sir Terry Pratchett; J.R.R. Tolkien, Douglas Adams and of course, my favorite: Robert Rankin ("Hollow Chocolate Bunnies of the Apocalypse", "Armageddon - The Musical", and "Snuff Fiction", to name but a few).
If you never read anything by Robert Rankin: Imagine combining Adams and Pratchett, add alcohol and running gags and you might get something which is almost entirely, but not completely, unlike Robert Rankin.

Harry Potter Series
LotR Trilogy
The Old Man and the Sea (Hemingway)
Absalom, Absalom! (Faulkner)
The Red Pony (Steinbeck)
Winesburg, Ohio (Anderson)

Those are a few off the top of my head. I'm something of an eclectic reader, though... I have a lot of trouble enjoying any books that I don't find to be artistically sophisticated, and as a result I tend to just default to "not reading."

Oh therea re a lot of books more artistically sophisticated than Harry Potter believe me:)

the mirror crack'd by agatha christie is great and of course DISCWORLD books!

Depends on your definition. Harry Potter is a top-notch children's fantasy with incredibly well-drawn characters, a well-crafted plot, an expertly done exploration of "childhood moving to adulthood," well-written prose, great pacing, and a believable and interesting world. No, it may not have anything particularly pretentious to say about the human condition, but for what it does it's very, very good.

Perhaps "artistically sophisticated" isn't the right phrase... it's hard for me to exactly define what it is I'm looking for, because there's a ton of classic literature that doesn't cut it for me either, as well as most modern fiction.

Exactly.

Ooh, maybe I should read Dune. I've never read it. What does it do well? What's the appeal?

I was happy to read the HP series and would recommend it to anyone, but have to disagree with you there. Potter 1 was an affront to the written English language and it amazes me to this day that editor might still have a job. And lets not get into pacing for the entire second half of the series. 5, 6, and 7 were borderline biblical at times.

Basically, what it does well is its universe, politics and general awesomeness. It will drop your jaw more than once, and at least once you'll think "Fucking hell that was the best thing ever!"

explain

Plot and story. If you like drawn out epics where the cogs grind into place, just the book for you. I never read the later ones in the series but the first few were good.

Shogoun - James Clavell
Mistborn trilogy - Brandon Sanderson
The Automatic Detective - A. Lee Martinez
Gil's All Night Fright Diner - A. Lee Martinez
The Dresden Files series - Jim Butcher
The Stand - Stephen King
Neverwhere - Neil Gaiman
Complete Stories and Poems of Edgar Allen Poe

I also like graphic novels:
The Walking Dead series - Robert Kirkman, etc
Batman: The Long Halloween - Jeph Loeb and Tim Sale
GTO series - Tohru Fujisawa
Sanctuary series - Sho Fumimura and Ryoichi Ikegami

The number of pure grammatical errors was staggering. And I dont mean the whole English/US English arguement. Certain sentences simply make zero sense. And throughout the series the deus ex machina she uses is usually considered the mark of a subpar writter. I mean the Potter/Voldemort double wand thing almost had me out of my chair... Again, I liked it immensly so i am not bashing it. But there are certain things it did not do well with and general prose was one.

It's been awhile since I read Potter 1... I was thinking more about the later books. But use of 'deus ex machina' doesn't fall under prose.

No, wondering thoughts on my part. Hence the reason I fail to be a billionaire author. Or just a decent one. Or even an author...