Man, I totally love this series. It ranks among the top of the lists for me.
I really like the way GRRM writes here, seems almost real. That and he's really good at making you love or hate characters (damn Cersie Lannister should die is the deepest pits of hell... the wench.)
But yeah, I've read the first three and I just got the fourth, but unfortunately classes get in the way with reading, so I might not get to reading it in a bit.
But as for what I predict/think. Jon Snow is not Eddard's son. But he is a Stark! I predict him to be the son of Lynna (Ned's sister) who was raped by Rheagar Targaryen. All through the first book, Ned is haunted by his memories of Lynna saying "Promise Me". I think the promise was to take care of Jon as well as have her buried in the Winterfell crypts (to cross reference you don't need to go far into the first book... like 45 pages).
As for what's going on in the south (and what I'll undoubtably find out in the fourth book) I bet Littlefinger has the throne on strings, but he's too clever to take it for himself. He'd just manipulate the man on there. That clever bastard.
What really interests me, though, is who will ride the dragons. Obviously the black is Dany's. I think Jon Snow/Targaryen/Stark will ride the green. And perhaps Tyrion the last. Never never never underestimate that man, he is cunning to the bone.
And poor Arya... I think that girl will eventually meet up with Nymeria... and they'll cause some big killing crazyness to go down. With both of them mostly mad and all.
Oh my... that was quite a rant, forgive me for being long winded... I'm trying to catch up on all I missed.
I just have one last thing to say "Long Live Sandor Clegane!"