I figured I might not be the only one who has not read the books, and who is a bit overwhelmed by all these families and their relationships among each other. So I figured we could use a thread that provides an overview, and where you can post any questions you have about the characters.
Here's what I have so far. Feel free to add and/or correct. As I said, I'm still trying to wrap my head around this.
Robert Baratheon, King of Westeros. Took the throne from a Targaryan king, and almost wiped out that family since they were responsible for the death of his love, the sister of Ned Stark. Has a son called Joffrey, who is supposed to marry Ned Stark's older daughter. Married to Cersei.
Cersei from the Lannister family has a twin brother called Jaime she's having an incestuous relationship with, and another brother called Tyrion who's a dwarf.
The Lannisters are said to have killed the 'Hand of the King' Jon Arryn, who was married to the sister of Ned Stark's wife Catelyn from the Tully family. They have a son.
Ned and Catelyn Stark have five children, three sons (one of them called Bran) and two daughters, Sansa (who is supposed to marry the King's son) and Arya, who's a real tomboy. Ned also has an illegitimate son called Jon Snow, who lives in his household. Ned has a brother called Benjen who is a member (or even the leader?) of the Night's Watch that guards the wall to the North.
Viserys Targaryen wants to re-take the throne from Robert. To raise an army, he marries off his sister Daenerys to Khal Drogo, lord of a nomadic Dothraki tribe of horsemen.