Okay a book one issue that doesn't need to be spoilered. I just had a glance at the "westeros" forum and there was a long standing debate that seemed pretty darn cool.
Rhaegar + Lyanna = Jon Snow?
Think about it... it actually makes a lot of sense.
Book one only stuff...
Ned is protective about Jon and won't tell anyone about his mother (including Jon). He left for less than a year and comes back with a son... seems pretty out of character for Ned right? Ned resigns as Hand over Robert's desire/need to blindly hunt down and kill all Targayian children. "She's just a girl Robert, Let it go!" Lyanna was supposedly kidnapped and abused by Rhaegar. Robert says it was rape... but was it? Maybe Lyanna actually loved him and eloped willingly. And even if it was rape who is to say there wasn't enough time for Lyanna to have a child. And we already know that the Lannisters and the Targaryians only stay blond because they are into incest 
and when confronted with dark haired genes they have dark hair so we have Jon.
Did anyone think of this on their own. I certainly didn't.
Came to mind alright, key issue is both Ned's memory and the story told to Bran about the tournament at Harrenhal, Rhaegar won it and gave the crown of love and beauty (terrible name) to not his wife but Lyanna, now we don't know yet if the feeling was mutual but from what we're told about Rhaegar he comes across as sane (unlike his father and brother) and doesn't seem the type to kidnap and rape a woman and Roberts view of it can be at best described as biased. Also Arya's been compared with Lyanna by Ned so its possible she could be headstrong enough to elope
Now Neds view of Targaryen children could be influenced by this but his own personality alone could account for that in not wanting to assassinate innocents.
Unfortunately the only person alive who knows for certain is Howland Reed as he was the only other person than Ned who survived the Tower of Joy (another question why the hell was so many of the best of the Kingsguard there and not with Rhaegar, Aerys or Viserys and the pregnant with Daenerys Queen at Dragonstone, all more logical places for them to be)
