I was never entirely convinced, mostly because that would favor Jon Snow too much. But I have to say, the hints are pretty heavy. So the only reason I am expecting this theory to be false because I am internally waiting to be shocked.
However since I am not an actual believer in the theory, I cannot ignore some plot holes.
Most pro-RLJ argue that Ned only ever thinks about Lyanna and never the mother of his bastard, he also never *hardly* thinks about Brandon, his father and never even, seriously never, thinks about his mother.
And Jon Snow is northern to the bone. I get that children in westeros seem to favor a parent entirely, but he's too northern, too much, that even if he's Rhaeghar's son, I can never imagine anywhere without snow.
I believe "Snow" is his identity. And North. And he has a freaking werewolf he can warg, now if he also would own a dragon (and suppose he could warm it too), it just becomes very uncharacteristic of him.
He may be the son of Lyanna and Rhaeghar. He may be the song of ice and fire. But he is more ice. And will always be ice.
(plus even if I do buy the RLJ theory, I can't except that Lyanna ran away. And if she did, I hope no one ever finds out. Too many people died of her and Rhaeghar's foolishness. And just a sidenote Rhaeghar is such a depressed soul)