Brandon Stark
Ned's wild elder brother, once heir to Winterfell and betrothed to Catelyn Tully; a name spoken of but never seen.
The fuller tale
Every generation of Starks, Old Nan might say, has a child with the wolf blood — the wildness that runs hotter than the North is supposed to allow. In Ned's generation it was Brandon: the eldest, the heir, the brother people meant when they said a Stark was handsome. He was a superb horseman and a better swordsman, betrothed to Catelyn Tully, admired and a little feared, and possessed of exactly the temper his careful father's careful plans could least afford.
The tale meets him only in other people's memories, and the memories disagree in instructive ways. To Catelyn he was the gallant almost-husband, the life she was promised before she was handed his quieter brother. To Lady Dustin, who loved him and lost him to politics, he was a man who took what he wanted and laughed about it. To Ned he is mostly silence — a grief filed next to Lyanna's, too expensive to take out and look at.
It was Brandon who, hearing that Rhaegar Targaryen had carried off his sister, rode straight to King's Landing with a handful of companions and shouted at the Red Keep's gates for the crown prince to come out and die. It was brave, it was magnificent, and it was precisely the wrong thing to do with a king like Aerys listening. The wolf blood, Ned reflects long after, took both his brother and his sister to early graves — and made his own patience the thing that kept House Stark alive.
The page and the screen
The show grants Brandon perhaps two sentences across eight seasons; viewers could be forgiven for forgetting Ned had a brother between Lyanna and Benjen. The books make him a small but load-bearing ghost: Catelyn's chapters measure Ned against him, Barbrey Dustin's grudge against the Starks begins in his bed, and the rumors around Ashara Dayne at Harrenhal attach to him in some tellings rather than to Ned. He is the books' first demonstration of a recurring thesis — that the dashing elder brother dies and the dutiful second son inherits the story.
Their fate — if death has found them, it is written here. Open at your peril.
Before the tale: Died before the story
Brandon's ride to King's Landing ended in a treason charge — 'come out and die' being poor legal strategy under Aerys II — and his father's summons south ended in the throne room. The Mad King's idea of a trial gave Lord Rickard to the fire and gave Brandon a strangler's cord and a sword placed just beyond his fingertips. He died reaching for it. The books put the account in Jaime Lannister's mouth, a Kingsguard made to stand and watch; the show leaves the scene as a line of Ned's, which is roughly how Ned would have wanted it.