X'nedra, after reading Tolkien, Eddings was one of the first authors I found. I probably read The Belgariad three times in high school. I enjoyed the great quest the characters undertook. Later I moved along to Raymond Feist's Riftwar Saga. The characters quest against a background of political scheming and divine conflict. Back then I would not have wanted to read GRRM's A Song of Ice and Fire where there are only a few questers among dozens of major characters and where greed and avarice in greater supply than honor and sacrifice.
Tolkien set the stage by telling his stories as mythology from a long, long time ago. Eddings and Feist moved a bit closer to the action, but did not really take the shine off the heroes nor the goodness from the stories. Martin, on the other hand, tells us the story from the characters' points of view... e.g. showing us how the prince and the princess turned out and not giving us a moral embellishment. All in all, there are surprises galore.
And as hadd mentioned, there are great characters. For instance...
If you were ambivalent about King Arthur, you'll like King Robert.
If you liked Guinnevere, then you'll love Catelyn and Sansa.
If you hated Guinnevere, then you'll loooove to hate Cersei.
If you liked Lancelot, then you'll love to hate Jaime while you love the Blackfish.
If you liked C'nedra, then you'll love Arya and you'll love to hate Sansa and Cersei.
If you liked Garion, then you'll like all the sons of Eddard Stark.
If you liked Silk, then you'll love the Imp.
If you liked Bilbo, then you'll love the Imp.
If you liked Gandalf, then you'll love the Imp.
If you are human, then you'll love the Imp.
If you can't guess, I love the Imp!
You know how some series have appendices in the back or lists of characters in the front to assist you in keeping the characters straight? Well, with ASOIAF... forget it. The named characters number in the thousands... Characters with dialogue must tally a thousand... There must be about one hundred characters essential to the story... And the main characters number around three dozen... All in all it is mind boggling.
There are two caveats to beginning the series...
First, GRRM does not make rampant use of non-human races. He does not feature a plethora of battle-wizards and magic swords. There aren't any elves, dwarves, orcs, snarks, or grumpkins... This is not a fairy tale in any way, shape, or form.
Second, Martin takes his time to craft each an every book. It is my understanding that he began writing this story in 1991 as a trilogy. He's been writing for nineteen years and has published four books of a now planned seplogy (Is this a word? If it's not, can I get it trademarked? Uh, what I meant is that GRRM plans on seven books for the series.) Anyway, the books were published in 1996, 1998, 2000, and 20005. The next book should be published in 2011... but we don't know that yet. My warning to you is... If you cannot wait five years between books, then don't get started. My question to you is... Even with a five year wait, how can you not read the best (in my opinion... and I've read The Lord of the Rings about forty times) series out there?
In conclusion... If you're looking for something a little more than a fairy tale, then ASOIAF may be for you. If you're looking for something a lot more than a fairy tale, then ASOIAF is almost assuredly for you. If you're looking for good writing, outstanding storytelling, brilliant characters, and a fantasy story that you could in all conscience recommend to an adult friend who's never read fantasy, then ASOIAF is most definitely for you.
But don't take my word for it, try A Game of Thrones. Pick up a secondhand copy of the paperback, if you're not intrigued by page 85, if you don't think "No waaaaay that just happened!" by page 85, if you don't think "Up Starks! Down Lannisters!" by page 85... then just quit. But you'll miss the absolute shocking moment on page 727.... you'll miss the moment over your lunch break when your co-workers all stare at you as you shout "NOOOOOOOO!!!!" when you read page 727. And most of all you'll realize, "I should have seen page 727 coming... all the signs were there." And then you'll think, "What other signs have I missed? What else is going to happen?!?!" And then you'll be here with us posting, "Do you think?" "What about this?"
Finally, I cannot strongly advise you enough to avoid reading anything more, anywhere regarding ASOIAF. Martin is great at building suspense and you don't want to ruin the surprises... big or small.