I just started reading these myself. I like how the series is the direct opposite of most fantasy books where the protaganists ALWAYS get through horrible shit unscathed. Major characters die, or progress beyond the usual iconic status quo. What I don't like is how each chapter is a different character's point of view. There are so many, and they all are so damn good that I don't want each ones particular POV to end just yet. That just goes to show how well written it is.
I'm halfway through Storm of Swords right now and looking forward to Feast of Crows, but I've read many places that it may be the weakest of the series.
So far my fav characters are Arya and Tyrion.