Whose sword did Jon Snow use to kill the White Walker in Game of Thrones S05E08?
In episode 9 of season 1 ("Baelor"), Jeor Mormont gave Jon Snow the Valyrian steel sword, Longclaw, in thanks for saving his life from a wight.
In the books, it originally had a bear's head as the pommel, but Mormont had the pommel refashioned into a wolf's head of pale stone with ruby eyes for Jon. It's a "bastard" or hand-and-a-half sword (half a foot longer than a longsword), rather than a longsword or greatsword. It is the Mormont sword in the way that Ice was the Stark sword. Jorah Mormont inherited it when his father took the black, but had enough honor to leave it behind when he was exiled in disgrace for trying to sell poachers into slavery, and Maege Mormont (Jeor's sister) who now rules Bear Island, sent it to Jeor at the Wall.