Ramsay Bolton needs to die. After terrorizing just about everyone he's ever gotten his hands on, Ramsay has proven himself to be the worst of the worst in Westeros – and he's had some stiff competition. Watching a jerk like Ramsay get his comeuppance would be the height of narrative satisfaction, but who exactly will deliver that fatal blow? Sansa and Theon probably have the most cause to do grievous harm to Ramsay, but there are really any number of possibilities. Now that Jon Snow has left the Night's Watch, he might be taking more active steps in protecting the family he has left, especially now that Rickon is in Ramsay's clutches. Will Jon kill Ramsay on Game of Thrones?
Please, Jon, just end him. Though Jon took his vows seriously as a member of the Watch, his death means he is no longer bound to them. While he's been up at the Wall, his father and brother have been killed, his sister taken hostage, his other siblings disappeared. Considering Jon's ingrained Stark sense of honor, he likely won't want to let those things pass now that he's in a position to do something about it. Now that he's left Castle Black, anything is possible.
A battle is brewing between Jon and Ramsay for more reasons than simple revenge. Jon's decision to bring the wildlings past the wall has had deadly repercussions once already, and it turns out the other Northern Houses are as unhappy about it as the Night's Watch was. Smalljon of House Umber sought Ramsay's help in overcoming Jon and the wildlings, and Ramsay already has a vested interest in doing away with Jon to secure his seat at Winterfell. There's a lot of bad blood between the two, and it seems like that might come to a head in season 6.
Ramsay and Jon might come to blows in a potential battle dubbed "Bastardbowl" by fans. Trailers for the season have shown glimpses of an upcoming battle where sigils of Northern Houses (among them Boltons and Umbers) were visible and wildlings were present. This battle would determine the fate of the North, though let's be real, Jon definitely has more of a claim on Winterfell than Ramsay, Targaryen or not.
If the Battle of the Bastards comes to pass, then Jon will have both motive and opportunity to take Ramsay down. And honestly? It can't come quickly enough.