Isaac Asimov - Foundation Series - they’re pretty good.
If you’re looking for light reading, and a sense that good will prevail (what drew me to the Potter series) I’d recommend the Odd Thomas series by Koontz. Occaisionally gory, but no horror per se.
I have looked at a couple of these, but was not in a Dean Koontz mindset, so didn’t even try. I’ll give it a go!
Definitely GRR Martin, but 'ware the frustration. **silenus **is correct that there’s a chance he’ll never finish the series, and there will be much gnashing of teeth.
We wants more, oh yes we does, precious.
Another vote for Discworld…
I’ve just been introduced to Robin Hobb and have enjoyed the first two of her latest trilogy called Soldier’s Son. (and in finding that link I find that Robin Hobb is just one of two pseudonyms used by the author, Margaret Astrid Lindholm Ogden - goody, another author to discover!!)
I recently read the Ender series by Orson Scott Card - it was pretty damned good. It lead me reading other Orson Scott Card books, and I liked those, too. I was going to suggest The Dark Tower series by Stephen King (I just finished it), as it is very good, but if you’re King’ed out for the moment, maybe at some point in the future. 
I liked the Horseclans series by Robert Adams. They don’t seem to get much love around here. The premise is a post-nuclear war reversion to medieval society, with immortals and telepathic animals mixed in.
Finished all the King books - including Dark Tower series! Have re-read the whole series as well. (I am a chronic re-reader for books that I enjoy, and I loved that whole series.)
John Maddox Roberts has a series about a young politician/roughneck/“hero” who gets in trouble a lot and has to solve crimes in the Rome’s late republican era (about a decade or so before events of the HBO miniseries “Rome”)
Really good stuff. And short. Books are barely 200 pages.
Also:
A big yes on Discworld.
Re: A Song of Ice and Fire. Starts off great. Really great. Then spins its wheels.
Very similar, but etter than J.M Roberts (IMO) is **Steven Saylor’s **Gordianus series. Starts with Roman Blood and goes on for something like 15 books. I love this series and cannot recommend it enough for anyone who likes historical detective stuff, Roman history or just plain old good stories.
Lately, after seeing Avatar, I have been suggesting the John Carter of Mars books. Sure they’re a bit old but you will see where a lot of Hollywoods ideas came from and they are damned fine stories if you remember that, while some of the ideas seem cliche’ that is because they have been reused by others so many times.
Robin Hobb already mentioned, but am popping in to add her Far seer books - 3 series of 3 starting with Assassin’s apprentice.
Also you could try Katharine Kerr’s (now finally complete) Deverry series. I personally prefer the 1st set of 4 books, but the follow on series are still good, if not as good.
Mary Stewart’s Merlin books.
Now that the last 2 books have publication dates ( and the original author is dead, and can make no more additions) I would suggest The Wheel of Time by Robert Jordan (and now Brandon Sanderson, writing from Jordans notes and outline). Skip the last 3 by jordan, Nothing happens!! finish book 8 then read the plot synopsis for 9, 10 , and 11. More plot happens in book 12 then all 3 of the last.
If you enjoy alternate history/Fantasy try S.M. Stirling’s “Dies the Fire” trilogy and the 4 book series “The Sunrise Lands” set in the same world.
There is also “The Island in Sea of Time” trilogy which is a sepaerate but related parallel story.
or
If you can find 'em, the Wild Cards books are entertaining. George R.R. Martin edited most of them; most books in the series have more than one author. Some of the authors are quite big names, such as Martin himself, Roger Zelazny, Melinda Snodgrass, and Chris Claremont.
They’re “alternate history” books, involving the release of an alien virus over New York in 1946. Out of every hundred people infected by the virus, 90 will die, nine will become “Jokers” (mutants, sometimes quite hideous), and one will become an “Ace”, with a useful superpower. The interplay among the various characters, and what they do with their new-found burdens or bonuses, makes the series worth reading.
All the titles are card-related phrases. The series starts with Wild Cards, then Aces High, Jokers Wild, and so on.
If you are interested in fanatasy and worried about Martin never finishing his series, I highly, highly recommend Joe Abercrombie’s First Law series:
What I like about it is that it is well and entertainingly written, with truly interesting and memorable characters and a plot that hangs together and makes sense. It isn’t hugely innovative but reads like a breath of fresh air.
Of course you should read Tolkien’s The Hobbit, then The Lord of the Rings, then The Silmarillion, and then Unfinished Tales, if you haven’t already. Not a series, as such, but a great set of interlinked books set in a fantastically detailed Middle-earth.
I’ve recently started the Japanese “Haruhi Suzumiya” series, as it is just now being translated into English. Look here for the list (the list is close to the top of the page), as you can see, only the first two are available now, but the third has a release date and the others will be coming: http://tvtropes.org/pmwiki/pmwiki.php/Main/SuzumiyaHaruhi
I don’t want to be spoilerish, but it involves Haruhi Suzumiya, who is a high school student who is easily bored and wants nothing except to meet and hang out with aliens, time travelers, and ESPers. Her and the narrator start a club at their school with that purpose in mind, get a few other members and then start looking. However, unknown to Haruhi but revealed to the narrator, they may have already discovered them. Also unknown to Haruhi but known to the narrator, it is vitally important to keep her happy, or there could be dire consequences for the universe. It’s pretty funny, and kind of smart too, probably geared for a younger audience.
Do be careful and get the actual novels (called ‘light novels’) rather than the manga though. The covers of the two I have are a solid bright colour and do not have a picture of any characters (well, except maybe a small silhouette) on them, if you’re getting them from online.
Fantasy:
Lois McMaster Bujold, either her Vorkosigan books (sf) or her Chalion books (high fantasy). Bujold is kickass. Yes, that’s the technical term.
Robin Hobb, start with Assassin’s Apprentice
Jim Butcher. I didn’t really like the first Codex Alera book, so I might not finish that series, but the Dresden books are really entertaining.
Patricia Briggs’s Mercy Thompson books, starting with Moon Called.
Kristin Cashore’s Graceling and Fire.
Suzanne Collins’s Hunger Games and Catching Fire.
Historical mystery:
CJ Sansom’s Matthew Shardlake books, starting with Dissolution.
Fiona Buckley’s Ursula Blanchard books, starting with To Shield the Queen.
And just to throw a monkey in the wrench:
The President’s Daughter, by Ellen Emerson White. About the daughter of the first female president. This series blew me away.
Another vote for the Pratchett/Discworld books.
I read ‘Night Watch’ first, and it’s a great stand-alone, I think. Then, after you read more of the others and re-read it, you get even more of the inside jokes.
Got my S/O hooked on Discworld by starting him on that one too.
Another vote for Butcher, and Hobbs’ Farseer series is probably my favorite ever of the genre, I couldn’t even say why, even though I started that one backwards and read the last 3 first.
Not a series, but Wilbur Smith’s River God is a WONDERFUL historical escape fantasy. I would like to call it historical fiction, but to be frank I do not know Smith’s reputation regarding facts entered into the fiction. However, every last detail is more than plausible; I would LOVE to see this made into a movie.
HBO could carry this over a week’s worth of nightly episodes, easily. It’s grand, it’s got the requisites of blood, love and rhetoric; it’s just a great read. And if anything’s remotely ‘true’ regarding the Egyptian culture and engineering, then it’s a fascinating look at that time period, as well. Wow…forgot how much I liked this book! It’s not heavy reading at all; a great curl-up novel that takes you out of your head for a good while.
Same thing happened to me, but I tried the second one anyway and just scarfed my way through the rest of them. There are now…5 or 6? So I get my Butcher fix twice a year: a new Dresden in May and a new Codex in November.
And I’m tagging this thread for future trips to the bookstore!