Reading the books will give you background on the characters and help you keep the enormous cast straight in your head. Also, the show doesn't follow the books entirely (but I like where they've taken it), and many fans anticipate the show going in its own direction in at least some story lines.
Also, reading the books will help you get a better understanding and/or appreciation of some of the stuff that goes on, why it happened, and what characters were doing/thinking/feeling when it happened.
That being said, the show can be enjoyed very thoroughly as a stand-alone thing.
In conclusion, I'd say read the books if you want to go really in depth into the story and see specifically in which ways the show is different from the books. It's a huge time sink to read all the books, but I loved it!