7. The Foundation Series by Isaac Asimov
Not at all alike. Extremely dry, without character continuity. It's basically like a series of morality plays on socioeconomic forces in the beginning. Gets Dark Tower'd later on.
Main similarity to ASoIaF is that they both start out pretty grounded and get progressively more supernatural, though it ASoIaF this feels planned whereas in Foundation it seems more like a retcon.
Only worth reading the first book; in fact, reading later books will undermine enjoyment of the first book.
11. The Dune Series by Frank Herbert
First book has a pretty similar plot and tone to AGoT. It's not very accessible; for people who feel like the early bits of Fellowship of the Ring or AGoT are inaccessible, this is far more so. The first time I tried reading it in middle school I wasn't able to make it very far.
The series changes tone and gets a lot more abstract and philosophical in later books. May be interesting to continue if you really like the speculative nature of sci fi.
12. The Hyperion Cantos by Dan Simmons
Can't really think how this is like ASoIaF...
I do appreciate that it addresses time dilation, which is something most science fiction runs away from, though I wouldn't go so far as to say it's hard sci-fi. Series gets boring after the first book.
Interesting how all of these series peak in their first book.