I too thought like this. I came across the story when GoT debuted on tv. Watched the 1st and 2nd seasons and thought i'd only get the books at the end, not to spoil the experience. But then I came across a huge promotion on the complete collection of the 5 books, bought them and read them all in little more than one week.
Oh boy, how I was wrong. There's a myriad of details that the series don't tell or are too subtle that only someone how read the books will notice that it blew my mind.
More recently, when the 3rd season arrived, I watched it all from the beginning with my GF, so i could get her hooked on the show, and it just made for a better experience. Plus it gave me an entirely new view on all the crazy theories (lr=j, i'm looking at you).
Plus, how can you watch all the episodes out so far and not want to know all that is publicly known about the story so far? (even more with that cliffhanger almost-ending that was the red wedding)