You know, for a fantasy series, A Song of Ice and Fire doesn't have tons of magic. In plenty of fantasy, the magic is front and center. Magical creatures, magical people, magical wars, magic, magic, magic...
But, Martin plays it subtle. In most of the first book, there's hardly anything magical at all. A hint here and there, a couple of ghost stories, but nothing major. Granted, it gets bigger as the series continues and more of the supernatural crops up. But, as a part of world-building, Martin really treats magic as many other writers would treat electricity in a modern setting. It's useful, it can affect characters and plot, but it's not the main attraction.
It's an interesting choice. Why'd he do it?
My theory: I think it's because Martin is really interested in historical fiction and he wanted to write a historical story. Doing it in the fantasy genre allowed him to hold on to all the fun stuff with historical fiction, yet mix it up a bit by creating his own settings, politics, religions, etc. In a sense, I would almost call the series less a fantasy series and more a historical fiction series that just happens to be set in a world that Martin made up.
The payoff: In fantasy, as with any other genre, there are those who do it well and those who do it poorly. When fatansy is poorly written, the magic becomes the be-all end-all and it sets up deux ex machinas and all of that other nonsense that happens just because it's convenient to the story. Why did the character do that terrible thing? He was cursed! It's not his fault. So, you get the terrible act, but no real consequence, because he's absolved of guilt. Poof! Done. Boring.
When you downplay the magic, and use it to make problems instead of solve them, then you're making life more complicated for your characters. When you look at Martin's books, the cost of magic is high and you don't always get the outcome you expected. Usually, characters who get tangled up with magic find themselves in more trouble than they started out in. They have to fight harder, struggle more, and in turn, we get more invested.