First of all, I would like to say that I cannot take credit for this theory. Most of this has been formulated from my own opinions from the book series 'A Song of Ice and Fire', other formulated theories on various forums, and the last piece of the puzzle was dropped on my lap by a good friend.
Firstly, the question of who is Jon Snow's mother needs to be answered. For those who are aware of Ned Stark's unquestionable honor, the mere thought of him bringing home a bastard after Robert's rebellion is kind of a big deal. Like a really big deal. The name of his mother is not given, yet throughout the first book Ned is haunted in his dreams about his last encounter with his sister Lyanna while she was on her death bed. The phrase "promise me Ned" comes up several times. What could this promise be exactly? Personally, I think that Lyanna asked Ned to look after her child... that child being no other than Jon. But if that's the case... why the shame? Why the secrecy? The next question that comes to mind is who is Ned's father. Though Robert was destined to marry Lyanna... she was "stolen" by Rhaegar and than presumably raped by him... or at least according to Robert. Numerous testimonies throughout the series from people other than Robert claim that he wasn't actually that bad of a guy... arguably a pretty stand up dude. Now considering Robert's hatred for Targaryens...this is good reason to hide the identity of Jon from the rest of the world. Mostly due to the fact that there is a good chance Robert would kill Jon for simply being Rhaegar's son. So the promise Ned made to Lyanna was to take care of her son and raise him as his own. So to protect the child Ned convinced the world that Jon was his bastard. Furthermore, there are numerous refrences in the the first novel of Ned claiming "he/you[jon] has my blood". That would be true considering Jon is Ned's nephew. So there you have it Jon is a Stark (ice) and a Targaryen (fire) [a song of ice and fire] [It also solves the mystery of who is the third head of the dragon prophecy]. So not only is Jon now a Targaryen... he technically has a claim to Iron Throne... possibly more so than Daenery's. But oh wait... the last book ended with a couple members of the night's watch going Ceasar on his ass... with him being presumably dead. I mean the guy did get stabbed for times (at least). It's a shame that no characters in the book have the power to bring people back from the dead. Oh wait? That's right the Red Priests do, I mean they did for Catelyn Stark (aka stone lady). But how can he become a King if he is in the Night's Watch? I mean it is an organisation that you stuck with for life.
"Night gathers, and now my watch begins. It shall not end until my death. I shall take no wife, hold no lands, father no children. I shall wear no crowns and win no glory. I shall live and die at my post. I am the sword in the darkness. I am the watcher on the walls. I am the shield that guards the realms of men. I pledge my life and honor to the Night's Watch, for this night and all the nights to come."
"It shall not end until my death". But what happens if you die and come back to life??? It doesn't specify you have to spend all of your lives on the wall once you take the black... just that it end's once you die. So if Jon dies, comes back... isn't he free from his oaths since he did fulfill them to the letter... by dying and all. So that would leave him free to... I don't know rule the seven Kingdoms wouldn't it?
And that's my theory. Don't know how it's going down but it will. Jon is Targaryen and Stark, he dies(as we all know George is more than happy to kill of our fav characters... and sometimes bring them back from the dead) and comes back to life, get's an army somehow and some support from the other family's and comes riding in at the last moment to save everybody's ass.