We now know for certain that Rhaegar Targaryen and Lyanna Stark are the parents of Jon Snow (well, on the show, at least). YouTube user hurleybird painstakingly collected every single scene and mention of them on the series so far, and assembled them in one moving masterpiece of a supercut.
Source: io9 – You Must See This Supercut of Every Clue About Jon Snow’s Origin From Game of Thrones