I haven't read the books yet, but my question is why wasn't Ned Stark king instead of Robert Baratheon? Was it because House Baratheon was more powerful than House Stark?
The queen stood. "And what of my wrath, Lord Stark?" she asked softly. Her eyes searched his face. "You should have taken the realm for yourself. It was there for the taking. Jaime told me how you found him on the Iron Throne the day King's Landing fell, and made him yield it up. That was your moment. All you needed to do was climb those steps, and sit. Such a sad mistake."
"I have made more mistakes than you can possibly imagine," Ned said, "but that was not one of them."
A Game of Thrones, Eddard XII
Ned never wanted the Iron Throne for himself. Especially since, as Dan pointed out, Ned's good friend Robert had the better claim.
Essentially Robert had the better claim.
The Family Tree here shows that his paternal grandmother was a Targaryen and thus his claim was solid.
In fact there are no significant marriages between the Starks and the Targaryens, so Ned had no "claim" to the throne. It's also abundantly clear that Ned did not want power for himself and had no interest in politics.
Lord Eddard Stark is/was an honorable man. He loved Robert as his brother much as he loved his flesh and blood. He fought side by side with Robert not for a kingdom but for Justice. The kingdom was secondary... Once justice was served, Eddard saw no need or want for the throne. He simply wanted to go back North with the remains of his family and offer them a proper burial among the dead below the castle of winterfell. Also, Eddard would have respected tradition and the fact that Robert had a claim to the throne... Eddard did not.
Ned's sister was in love with Robert, and I suppose Aerys killed her. Then Ned's big brother Brandon asked for revenge, and he got also killed. So the Bareathons started war, not for being Targeryan, but for revenge and to end the injustice. Ned supported him because Robert was his best friend, and was fighting for his sister. The throne was not what he was looking for in his life, not even for Winterfell. He became Lord of Winterfell just because his older brother died.