According to the books so far it is between Lady Dayne and common woman called Wylla as far as I remember
I'm remembering the woman Wylla too, but I wouldn't put it past GRRM to pull a fast one out of his hat ...
I think it's Lyanna Stark--and that's where his looks come from. And his father is Rheagar Targaryen.
Now, I should point out that I'm only halfway through book 3, so I could be proven wrong. But I am pretty sure that that is where this is going. Think about it: Lyanna died in a pool of blood (childbirth), and Ned had to fight the Kingsguard to get to the tower. Why would the kingsguard be there if not to protect an heir? When Robert was dying he said that Rhaegar ultimately won, because he got Lyanna, and at some point Ned said he'd been living a lie for 14 years. I really think the "Promise me, Ned" that Lyanna was pleading as she died was for him to take the baby and keep him safe, lest Robert try to kill him as a Targaryen heir.
This site gives some more details as well :)
http://www.angelfire.com/ma4/mlarchives/faq/jon.html
This was very interesting reading. I look forward to finding out who his real parents are. I have just started book 4.
I also think Lyanna is Jon's mother, and agree with those who think Prince Rheagar is his father.
Who do you think Jon's mother is?
I really think it was Lyanna... who do you think and why?