How he goes out: Theon had one of the most depressing character arcs on this series, so we're at least happy that he dies an admirable death while trying to protect Bran in the Godswood. After all the other members of the Ironborn fall around him as the wights invade, Theon is able to keep expertly taking out the zombies with arrows (and then when those run out, he starts slaying them left and right with his spear).
He's the only reason why Bran survives up until the very end, since the Night King arrives just after Theon has killed all of the attacking wights. Theon accepts his fate after Bran tells him he's a "good man," and charges at the icy villain with his spear raised. He dies instantly of course, thanks to a sword through the chest courtesy of the Night King, but it's an act of bravery that we won't soon forget.