From "A Game of Thrones":
Bran thought about it. "Can a man still be brave if he's afraid?"
"That is the only time a man can be brave," his father told him. - GoT, 16
"I was eight when my father sent me to foster at the Eyrie," Ned said."Ser Rodrik tells me there is bad feeling between Robb and Prince Joffrey. That is not healthy. Bran can bridge that distance. He is a sweet boy, quick to laugh, easy to love. Let him grow up with the young princes, let him become their friend as Robert became mine. Our House will be safer for it." -GoT, 64
The greatest living knight was Ser Barristan Selmy, Barristan the Bold, the Lord Commander of the Kingsguard. Father had promised that they would meet Ser Barristan when they reached King's Landing, and Bran had been marking the days on his wall, eager to depart, to see a world he had only dreamed of and begin a life he could scarcely imagine." - GoT, 77
"You're not my son," he told Bran when they fetched him down, "you're a squirrel. So be it. If you must climb, then climb, but try not to let your mother see you." - GoT 80
"He looked deep into the heart of winter, and then he cried out, afraid, and the heat of his tears burned his cheeks.
Now you know, the crow whispered as it sat on his shoulder. Now you know why you must live.
"Why?" Brain said, not understanding, falling, falling.
Because Winter is coming. - GoT, 163
"Bran had always liked the godswood, even before, but of late he found himself drawn to it more and more. Even the heart tree no longer scared him the way it used to. The deep red eyes carved into the pale trunk still watched him, yet somehow he took comfort from that now. The gods were looking over him, he told himself; the old gods, gods of the Starks and the First Men and the children of the forest, his father's gods. He felt safe in their sight, and the deep silence of the trees helped him think. Bran had been thinking a lot since his fall, thinking, and dreaming, and talking with the gods." - GoT 572
"Broken, Bran thought bitterly as he clutched his knife. Is that what he was now? Bran the Broken? "I don't want to be broken," he whispered fiercely to Maester Luwin, who'd been seated at his right. "I want to be a knight." - GoT 580
"He's marching the wrong way, he thought. For an instant he wanted to gallop after him and shout a warnng, but when Robb vanished beneath the porticullis, the moment was gone." - GoT 581
From "A Clash of Kings":
"Of late, he often dreamed of wolves. They are talking to me, brother to brother, he told himself when the direwolves howled. He could almost understand them... not quite, not truly, but almost... as if they were singing in a language he had once known but somehow forgotten." - CoK 70
"He was old enough to know it was not truly him they shouted for--it was the harvest they cheered, it was Robb and his victories, it was his lord father and his grandfather and all the Starks going back eight thousand years. Still, it made him swell with pride. For so long as it took him to ride the length of that hall he forgot that he was broken." - CoK 324
"They will be bigger still before they are grown," the young male said, watching them with his eyes large, green and unafraid. "The black one is full of fear and rage, but the grey is strong... stronger than he knows..." - CoK, 333
"The wolf dreams are no true dreams. You have your eye closed tight whenever you're awake, but as you drift off it flutters open and your soul seeks out its other half. The power is strong in you." - CoK 523
"The stone is strong, Bran told himself, the roots of the trees go deep, and under the ground the Kings of Winter sit their thrones. So long as those remained, Winterfell remained. It was not dead, just broken. Like me, he thought. I'm not dead either." - CoK 969