I've heard speculation that Jon Snow's actual parents may be Rhaegar and Lyanna Stark, but in reading the books I'm not sure what evidence could be used to support this conclusion. I thought there might have been something in the conversation Davos had before being smuggled into White Harbor, but I couldn't stretch anything that far.
What evidence do proponents of this theory cite? Does any of it involve stuff in the texts or just sweeping generalizations of the characters' personalities (e.g. "Ned Stark is too honorable to father a bastard").