I know who Jon Snow's mother is.
Spoiler
All the clues you need are to be found in AGOT, with the extra hint in ASOS.
Spoiler
2. Any time Eddard recalls Lyanna, he remember, blue roses, the same blue roses that Rhaegar Targaryen gives to Lyanna when he declares her the queen of love and beauty. Danaerys has a vision of the Wall, with a blue rose growing out of it. (Jon)
3. In Eddard Stark's remeberances, he and six others face three warriors of the Kingsguard at a broken tower in Dorne, where Lyanna was dying "in her bed of blood". So I have to ask: why are three of the Kingsgaurd guarding a broken tower holding a dying woman, when they should be fighting on the Trident? They had been ordered there, of course. Why? To protect Lyanna from the vengeful Martells, who would have slain her before she could give birth. After all, could you see Gerold Hightower, Oswyn Whent or the Sword of the Morning as murderers? None of them would taint themselves by killing a woman.
4. This brings us to Ned's promise to Lyanna. Should Robert ever learn that Lyanna had ever had a child by Rhaegar, the child would first and foremost be a threat to the throne, secondly, roberts hatred of all things Targaryen would mean the death of the child. So, Ned would have to promise that Robert, and the world would never know the truth. How could this be true? See the conversation between Arya and Edric Dayne in ASOS. If Ashara was jon's mother, how could Edric not know? As Harwin mentions shortly after, neither Ned nor Ashara were promised to anyone, so there would be no shame in it! Yet Edric was led to believe that Wylla was Jon's mother!!! I believe that both Ashara and Wylla were blinds, so we would miss the obvious truth; that Jon was in fact the last male Targaryen. Edit- This could also mean that Jon was the prince that was promised....
In short, I belive Jon is the son of Rhaegar and Lyanna.
This of course leaves just one question, why did Ashara kill herself? Compounded grief, of course. The death of her brother, and being rejected by Ned Stark, who certainly would have been aware that with the death of his brother, the promise of marriage to the Tully's would mean he would have to marry Catelyn to keep the honor of his house....