At the risk of pulling a spoiler, I think 2 story lines in particular shit the bed something fierce over the course of the 5 books, namely Arya's and Daenaerys's.
That being said, they were still epic books. I murdered the first four in 8 days. 4000+ pages in 8 days is pretty beast, thus gripping content. I find the interest level tapered off as the story wore on though. Few storylines continued to stay interesting to me, save a few which I can't really mention without blowing a premature nut for all of you who haven't read it yet.