The Return of the King
The whole series is geared towards bringing down Sauron, so he's clearly everyone's antagonist. We still never see him directly, and we don't have a strong image of his physical form. But we do get some indications of his sense of humor: as Aragorn marches with his 6,000 troops to the Black Gate of Mordor, Sauron toys with him for a bit by delaying before opening the gate and exposing his massive, massive armies to overwhelm Aragorn's people. Sauron's sadistic humor turns out to be a bad move on his part, though. In focusing so much on taunting Aragorn, he never spots the two hobbits carrying the Ring of Power right into the heart of his own land.
Saruman was a big antagonist in The Two Towers, when he controlled an army of ten thousand orcs. But by The Return of the King, he mostly seems like an embarrassment and a shadow of his former self. When Gandalf and Co. come across Saruman as they travel from Gondor to the Shire, they see him looking tattered and dirty, accompanied by his hanger-on Gríma Wormtongue. He looks absolutely pathetic.
But then, right at the end of The Return of the King, Saruman returns as an actual enemy. It turns out that he is behind the oppression and exploitation of the Shire originally arranged by Lotho Sackville-Baggins and then carried out by Saruman's half-orc henchmen. Saruman may lose his power to do large-scale evil in The Two Towers, but he's happy to attack the hobbits on their own territory.
Frodo is the protagonist of the narrative of The Return of the King, but he is also his own antagonist. The reason we focus on Frodo throughout this whole series is because he's trying to destroy the Ring. But in The Return of the Ring, he can't do his job. He gets very, very close, but he ultimately claims the Ring for himself. If Frodo had beens allowed to hang onto the Ring, he might have been able to become the next Sauron (hard to imagine, but the power would have been there). He's only saved from becoming the novel's major antagonist by Gollum's sudden attack.