Wylla

Wylla is an unseen character in Game of Thrones. "Wylla" is pronounced "Why-luh", not "Will-uh".

Season 1
During a conversation between Robert Baratheon and Eddard Stark, they recall the names of several women they knew when they were younger. Robert recalls one woman whom he believes to be the mother of Eddard's bastard son Jon Snow, and Eddard confirms her name was "Wylla". He refuses to discuss the matter any further, even refusing to tell Robert what she looked like. Robert tells Eddard not to be too hard on himself (for betraying his wedding vows) as they were at war and could have died at any time. Eddard had earlier told Jon that he would tell him more about his mother the next time they met, although due to Eddard's later death this was not possible.

Behind the scenes
Ned Stark never even commented to Jon Snow if his mother is alive or dead, though the HBO Viewer's Guide for the TV series lists "Wylla" (name in quotation marks) as deceased.

Author George R.R. Martin has stated the he does know who Jon's mother is, though he hasn't revealed it yet (he insists he isn't making it up as he goes along but does indeed have her identity planned out). Martin has told some of the cast members on the TV series secrets about their characters which haven't been revealed in the books yet, however, he has only revealed things which their characters would logically know already (i.e. he didn't tell them if they'll die in a future book).

Actor Kit Harington, who plays Jon Snow, has stated that Martin therefore did not tell him who Jon Snow's mother is, because logically Jon himself doesn't know.

In the books
In the A Song of Ice and Fire novels, it is a mystery if Wylla is still alive and if she and Ned Stark truly are Jon Snow's parents. Jon Snow is universally acknowledged to be a House Stark descendant because he bears a striking resemblance to Ned at a young age, more so than any of Ned's trueborn sons.

Robert Baratheon recalls that Ned had told him once that Jon Snow's mother was Wylla, a common girl he had an extramarital liasion with during Robert's Rebellion, though Ned refuses to revisit the subject nor discuss it any further since it was his dishonor towards Catelyn.

Wylla was a serving girl in the retinue of Lady Ashara Dayne of Starfall in Dorne whom Eddard met seventeen years before the events of the series, on the occasion of a great tournament at Harrenhal. Catelyn Stark heard a rumor in Winterfell that Ashara Dayne herself was Jon Snow's mother, a rumor Eddard refused to comment on at all.

Edric Dayne, Lord of Starfall tells Arya Stark that Wylla, his family's servant since before he was born, is Jon Snow's mother. Dayne calls Jon Snow his "milk brother" as Wylla nursed him as an newborn since Dayne's own mother was incapable of producing her own breast milk. Arya makes a mental note to tell Jon Snow about Wylla the next time they meet.

Another person claims to have heard a rumor that Jon's mother was a fisherman's daughter Eddard met by chance during Robert's Rebellion. These conflicting rumors suggest that Eddard himself may have been spreading misinformation, perhaps to protect the true identity of Jon's mother and prevent reprisals against himself or Jon.