While obviously nothing is certain right now, Martin seems to be setting the pieces in place for a major twist with his mother being Lyanna Stark, and the father not actually being Ned but Rhaegar Targaryen. We know Rhaegar and Lyanna disappeared together (the historical assumption is Rhaegar kidnapped Lyanna, but this hasn't actually been verified and is completely against the character of Rhaegar that has otherwise been established), Lyanna's last words before dying of unknown causes were to Ned demanding a promise of him, and that 3 of the Kingsguard were at Lyanna's side when Ned found her in Dorne when Rhaegar was at the Trident (and the Kingsguard, much less 3 of them at once, serve ONLY to protect those of royal blood). Jon obviously is rising to great prominence within Westeros and being set-up to rally the defense against the Others (the likely 'final villain', much as there can be one in this setting), and Rhaegar prophesized his son would be "The Prince Who Was Promised" (if it's not Jon, there really isn't a 'fitting' end game ruler for Westeros, since Dany is supposed to be barren now and thus would leave no heir even if she makes it through all the way to the end, not that Martin is by any means certain to leave us a clean ending). There's also the fact that circumstantial evidence leaves Lyanna as the likeliest candidate for the identity of the Knight of the Laughing Tree from Jojen's story to Bran, where she then could have actually met Rhaegar in person when Aerys sent him to pursue the unknown knight.
All this, coupled with the fact that Ned was pretty much honor defined when it comes to stuff like commiting adultery and siring a bastard just after marrying, gives plenty of reason to think Lyanna and Rhaegar actually fled together, conceived Jon, and Ned came upon her and the baby Jon as she was dying from childbirth; knowing Robert would never allow a Targaryen to live, much less one born from the woman he was in love with, Ned claimed him as his bastard to protect him.