JON THEORY, HIGHLIGHT TO VIEW: I totally owe Laura for bringing this thought to my attention -- it didn't even occur to me -- but she tied it to the enigmatic "favour" Lyanna asked of Robert. Favour being that she was pregnant after being raped by Rhaegar, and she asked Eddard to raise the child as his own.
It sounds plausible enough, and leads into a nice "Jon is a rightful Targaryen and can rule the Iron Throne as the badass he is blah blah" ending which I can (so far!) picture. The only thing I can think of POSSIBLY going against it is that Jon is explicitly described as looking more like Ned than his trueborn sons do -- but then again, I can't recall what Lyanna was described like. I feel like there might've been a line somewhere saying that she bore a striking resemblance to her brother, in which case it still fits.