WARNING: If you're actively avoiding any information about what might happen in Game of Thrones, this might not be the post for you.
One of the most popular theories about Jon Snow's parentage is that he's the child of Lyanna Stark (Eddard Stark's sister) and Rhaegar Targaryen. And, from the hints dropped in the trailer for next week's episode, it looks like the show is about to confirm this theory.
According to the R+L=J theory, even though the "beautiful and willful" Lyanna was engaged to Robert Baratheon, she fell in love with Prince Rhaegar Targaryen and eloped with him to a place called the Tower of Joy.
Thinking that Rhaegar had kidnapped and raped Lyanna, Robert Baratheon rebelled and eventually became king. During the war, Lyanna died in her brother Ned Stark's arms shortly after childbirth. However, knowing that her Targaryen son would be in danger from the new king, she first begged her brother to take care of baby Jon and hide the truth of his parentage.