Next to Rickon Stark's comparatively graceful death, Ramsay's murder in the Battle of the Bastards was brutal. After torturing Sansa for months, Ramsay finally gets what's coming to him when she sics his own starving hounds on him. Twitter reacted to Ramsay's death in the most satisfying way, mostly because everyone is so glad to see such a monster go. And even though Jon Snow was the one who captured him in the Battle of the Bastards, it's Sansa who finally got to finish him off.
The Battle of the Bastards has a dozen twists and turns, with favor in the fight switching hands often. (Though, admittedly, the Bolton armies seem to be ahead most of the time.) Incidentally, the episode was directed by Miguel Sapochnik, who also directed the Battle at Hardhome, in case that gives you any idea of just how epic this showdown was. Eventually, The Knights of the Vale swoop in at the eleventh hour and rescue a surrounded Snow/Stark/wildling army, thanks to a raven Sansa sent to Robin Arryn on the advice of Littlefinger. With the Knights of the Vale keeping the Bolton armies at bay, Jon Snow, Tormund, and Wun Wun spot an unprotected Ramsay Bolton, overseeing the battle from above.
They charge him and he retreats to the castle, but Wun Wun breaks the gate in. Just as he's about to be overtaken, Ramsay calls off the fighting and agrees to one-on-one combat with a heavily beaten down Jon Snow. Ramsay, who hasn't seen any fighting yet, starts shooting arrows at Jon, who blocks them all with a Bolton shield he's grabbed. Jon finally catches up with the Lord of Winterfell and beats him within an inch of his life, only stopping when he spots Sansa. He apparently decides to leave the honor to her. Later, after Stark banners fly over Winterfell again, Sansa enters the dungeon where Ramsay is being held. She coaxes out his hounds, whom Ramsay has neglected to feed for seven days, thinking that he'd be feeding them Rickon and Jon Snow by now.
Instead, Sansa lets them have at it with Ramsay, who foolishly thinks they're loyal and would never attack him. Uh yeah, maybe before you starved them for seven days, you jerk.
They literally eat his face off, and with that, we are finally free of the terror and reign of Ramsay Bolton.