Game of Thrones is an excellent series of books (although it takes forEVEr for him to write the next book and it's not finished yet, so who knows how many years it will take to get to read the conclusion) but it is also extremely violent and graphic and difficult to follow, so definitely not suited to everyone's tastes.
Odd Thomas is a really fun series. He just recently published the last book of that series and wrapped it up very nicely. A bit smooshy....but nice.It's got lots of tension, good laughs, rich characters, and various philosophical points to ponder.
An old classic that I really enjoy and re-read every couple of years is The Count of Monte Christo by Alexandre Dumas. That's a book that you can dig your teeth into and chew on for a long time. If you've ever seen the movie, try not to think about it too much when reading the book, because other than the basic premise of the story, they don't have much in common, although I enjoyed both very much.
If you're looking for something a little edgy (not really sure what your tastes are beyond YA and other than Harry Potter, that's not a genre I'm familiar with) you might consider The Dark Tower series by Steven King. It's a little hard to get into when you start reading the first book, but after a little while, it will suck you in and not let you go. A very meaty series that will keep your reading heart busy for a good long time.