There has been a long going debate about Jon Snow's parents and as of now the R + L = J theory seems to be the strong contender. However after the season finale many people were wondering if it was worth discussing about the theory as Jon Snow died in the episode. It looks like we shouldn't give up yet as the casting calls for Game of Thrones season 6 indicate that we might come to know about Jon Snow's parents. The casting call for a legendary fighter has excited many people. Here's the description of the character:

"A man in his thirties or forties who is a great swordsman and a paragon of knighthood. He carries a hugely famous sword on his back. The show is seeking a very impressive swordsman for the role- the best in Europe, for a week of filming fight scenes for a season 6 role. His ethnicity/race isn’t specified, unlike many other roles."

It is speculated that this character might be Ser Arthur Dayne who is also known as the Sword of the morning. He used to carry the greatsword called Dawn on his back. So the description shows that it most is Arthur Dayne. However the interesting part is that he has long been dead, which means he will be part of flashbacks which might involve his fight with Ned Stark at the Tower of Joy. In the books, at the end of Robert's rebellion, Eddard Stark came to know that Lyanna Stark was being held in the Tower of Joy.

It was guarded by Ser Arthur Dayne, Ser Oswell Whent, and Lord Commander Gerold Hightower, all of whom were members of Kingsguard. Ned and his men attacked the building and in the end only Ned Stark and Howland Reed (Jojen Reed's father) survived. After Arthur Dayne was dead, Ned found Lyanna who was dying and she then asked Ned to promise something before she died. No one knows what the promise was but people speculate the Ned found her dying with her baby and she asked Ned to protect her son, whom Ned raised as his bastard.

 If all these speculations are true, we might get to see Ned Stark once again also also come to know about Jon Snow's parents.