Some of my very best reads are the Harry Potter series, Lord of the Ring trilogy and A Song of Ice and Fire series.
This is a series review with no spoilers :D
First off, let me just say that GRRM is an amazing storyteller (also my favorite author). He's created a whole new world with its own history with complex characters and wicked plot twists around every page. The character depth in the series is excellent making it very difficult to pick a favorite character. Even the characters that I love to hate are brilliantly written. I have highlighted my favorite quips and phrases from each of the books. There's so many cause GRRM is just that much of a badass writer! I love that the chapters are divided by giving each character their own perspective. This allows me to see the world through their eyes and then view that same scene through a different character's point of view. Unlike other fantasy books, the characters in ASOIAF are not purely good or evil. Not all characters are lovable but their actions are justified (in their minds, at least) even though it often affects the world and people around them in a negative way. It's a domino effect.
This an ADULT fantasy series. There is incest, rape, violence and war. Profanity abounds. This is all in accordance to the time and world that GRRM has created. If you have an aversion to any of those - maybe this isn't the series for you.
It has political intrigue where everybody has a claim to the Iron Throne and elements of magic which do not detract from the central storyline. Non-fantasy readers should give book 1 a try. There is little to almost no magic in the first novel.
Marvelous, epic, dark and twisted -- this is not an easy, mindless read. I really had to challenge myself to remember who all the characters were by reading the appendices in between books ... but ohhhh, how I love getting lost in the world of Westeros.
Prepare to invest a lot of time and emotion into the series. There are only five books out with two more still to follow. I really hope GRRM is able to finish this series. I HAVE to know how it all ends!