Harry and Dumbledore talk about it briefly at the end of Chamber of Secrets:
"So I should be in Slytherin," Harry said, looking desperately into Dumbledore's face. "The Sorting Hat could see Slytherin's power in me, and it -"
"Put you in Gryffindor," said Dumbledore calmly. "Listen to me, Harry. You happen to have many qualities Salazar Slytherin prized in his hand-picked students. His own very rare gift, Parseltongue - resourcefulness - determination - a certain disregard for rules," he added, his mustache quivering again. "Yet the Sorting Hat placed you in Gryffindor. You know why that was. Think."
"It only put me in Gryffindor," said Harry in a defeated voice, "because I asked not to go in Slytherin..."
(source: Harry Potter and the Chamber of Secrets, chapter eighteen, Dobby's Reward)
So it seems the Hat was very strongly inclined to place Harry in Slytherin, but Harry's intense desire to avoid that fate swayed it into placing him in Gryffindor instead.
