I am a Game of Thrones junkie. I have read all the books, seen every episode of the show and read GRRM's A World of Ice and Fire which lends a lot of insight into the GoT world and all of its history. There are several clues in that book too which fan the flames of the popular conspiracy theories.
One theory that I am 100% behind is that Jon Snow is the son of Lyanna Stark and Rhaegar Targaryen. Let me explain. We all know that Ned Stark is the most honourable man in Westeros. The idea that he would cheat on his new bride and had a bastard boy from the occasion just doesn't sound like Ned Stark. When Ned brought home baby Jon Snow after the Rebellion, he refused to answer any questions about his birth or his mother. He insisted on raising the child as his own and as a companion to Robb Stark, Ned's true born son. In all the years after, Ned never discusses Jon's mother with anyone; not his wife, nor Jon. Yet when King Robert asks about him, Ned casually mentions the barmaid , Willa. Why tell the King but not Jon or his own wife Catelyn?
Ned Stark is a terrible liar. His is honourable to fault. That is why he keeps the subject quiet. He can't give away the truth. King Robert actively went after the Targaryens after the rebellion with the goal of seeing them all wiped out so no one could challenge his claim to the throne. If he knew that Jon was the son of Rhaegar, he would have had him put to death. That would have caused a new war between Ned and Robert most likely. It's not until Jon is heading off to the Wall to join the Night's Watch that Ned says to him, "The next time I see you, I'll tell you all about your mother." Why doesn't he tell him right then? Why does he have to wait until Jon is in the Night's Watch? Because only after Jon is in the Watch is he truly safe from Robert. Just like Measter Aemon (a Tergaryen), a brother in the Watch is there for life and sworn to hold no lands or titles or father any children. It protects Jon from any possible ambitions of his own, if he knew who his real father was.
It seems that the best explanation was that Lyanna Stark and Rhaeagar were deeply in love. Rhaegar was handsome by all accounts, a lover, a poet, a singer as well as a fine warrior. His marriage to Ellie Martell was arranged by his father, the mad King. They had two very young children together but that may have been him doing his duty. He may never have really loved her. Lyanna was likewise arranged to be married to Robert Baratheon. He was a notorious drunk and womanizer who bragged about his bastards which he had several of even then. Even though Robert loved Lyanna, it was not likely mutual. When Rhaegar won the tournament at Harrenhal and presented the winter roses to Lyanna instead of his own wife who was present and in front of Robert and his father, the mad King, he set off the fued that started the rebellion.
According to Robert Baratheon (the winners write the history), Rhaegar kidnapped Lyanna and likely killed her too. Rhaegar was a lover and by all indications of his nature, he never would have killed the woman he loved. Its seems clear that they ran away together. Lyanna got pregnant. Rickard and Brandon Stark would confront the King to intervene causing the King to burn both of them alive. Ned Stark became Lord of the North and joined Robert's side in the rebellion. In order to bring the Riverlands onto their side, Ned married Catelyn Tully who was betrothed to Brandon Stark before his death. When Ned had his army assembled (presumably after several months) he left Catelyn pregnant with his first boy Robb. At the battle of the Trident, Robert killed Rhaegar. The rebels went on to King's Landing to take it along with some Lannister help.
Somewhere in there, Ned Stark meets with his sister, Lyanna. He does mention making her a promise to her on her death bed. But how did she die? Nowhere in the Song of Ice and Fire is there any mention of how she died. She was a young woman. The best explanation is that she died giving birth. Birth to who? Jon Snow. She makes Ned promise to protect her baby. Ned does the most honourable thing he could do, tell everyone that the baby is his own bastard. He brings home the boy to Winterfell along with the bones of his dead father, brother and sister which get buried in the Stark crypts.
That part seems straight forward. Death in childbirth is common throughout the story. Daenerys Targaryen's mother dies giving her birth as does Tyrian Lannister's mother giving him birth. Along with Jon Snow, the three are the principle characters in the story and might share that common bond. (I also support the theory that Tyrian Lannister is actually the son of the Mad King, Aeres II and Joanna Lannister and have good supporting evidence, making the three principles all half brothers and sisters, but more on that later).
I want to explore a new idea that came to me. It's a bit of a stretch but bare with me. I questioned Lyanna Stark's death. She was after all, young and healthy. Is it possible that Lyanna did not die? If so, where is she? Let's suppose that she was in love with Rhaegar and ran off with him. When Ned meets up with her, he is going to tell her that Robert killed Rhaegar at the Trident. If Lyanna truly dislikes Robert and wants to avoid marrying him and to protect her baby, Jon Snow, she has to go into hiding. This is where she makes the pact with her brother Ned Stark. She gets Ned to promise to protect her child which he does. She then makes him return home with the bones of a random dead woman (there was a war on, there would be plenty) and declare her dead. Like I said, there are no details of her death any where in the stories. This stops Robert from looking for her.
Where would Lyanna go to hide though? She can't go back to Winterfell, she would be recognized anywhere in the North. She couldn't go to King's Landing either, Robert is there? She would be recognized almost anywhere in Westeros. Perhaps she joins a Sept as a Septa? Still risky. Most likely, she would leave Westeros and go east. When would it be safe to go back? After Robert dies. So what happens to her in those sixteen years over seas? Where does she end up? What does she do? Where is the most remote place on the planet from Westeros? Asshai by the shadow at the far end of the Jade sea. Asshai is a mysterious place where knowledge, religion, and magic all flourish.
Let me jump ahead now. In book two, "A Clash of Kings" we are introduced to Millisandre, the red prietess. She shows up at Dragonstone with Stannis Baratheon's wife, Selyce after Robert's death. Selyce was in the free cites where she met up with and fell under Millisandre's convictions. Millisandre goes with Selyce to Dragonstone and converts Stannis as well by convincing him that he is the second coming of Azor Ahai. Millisandre manipulates the entire Baratheon family and has them wrapped around her finger. She convinces Stannis to buy everything she tells him. She helps him to kill his own brother Renly. It all eventually leads to the destruction of Stannis and his family. While she was with Stannis, it appeared that Millisandre's intentions were true. In retrospect however, it seems as though she could have been plotting the destruction of the Baratheon's house all along.
Millisandre is indeed a Priestess of R'hllor, the fire god. That much is certain. She claims to have been a slave named Melony once. She claims to be from Asshai. The problem I have is her appearance. People from the Jade sea are supposedly much like our Oriental people in appearance. They are generally short, black hair, slanted eyes, skin tone, etc that we usually associate with east Asian people. Millisandre however, is described as fair skinned, tall, round eyes, with bright red hair. It does say that her hair is "impossibly red" which means that she likely dyes it. Millisandre's age also about the same as Stannis, mid, late thirties which would also make her about the same age as Lyanna Stark if she were alive.
Millisandre was the one who convinces Stannis to go to the Wall. When Millisandre first lays eyes on Jon Snow, she sees something in him. Anyone else notice that stare on the TV show? She continually tries to get closer to Jon Snow. When Stannis goes off to Winterfell and his final demise, Millisandre goes back to the Wall and to Jon. She tries to warn him of the danger coming his way. Why does she abandon Stannis and why is she trying to help Jon? Some say that she realizes that Stannis is not the true Azor Ahai but thinks that Jon is. That does make sense. However, there could be another explanation.
What if Lyanna Stark is Millisandre? Lyanna runs away after the rebellion to Asshai. She ends up in the faith of R'hllor and learns all the tricks. She dyes her hair bright red. She heads to the free cities and where she meets up with Selyce Baratheon. She easily manipulates her. When she hears about Robert's death, and her brother Ned Stark's death, she heads to Dragonstone to manipulate Robert's brother and heir, Stannis. She plots the complete destruction of the Baratheons. She convinces him to go to the wall where she finally meets her son for the first time in about eighteen years, Jon Snow. There would be no one alive who would recognize her. Her age and her disguise help as well. She definitely has a major interest in Jon Snow which is what makes me believe it.
Think about it.
One more thing while I'm on a rant about Game of Thrones.
Be ready for this to happen in season six of the show and in book six,
Remember that you heard it here first.