The Two Towers
Sauron is the Big Bad in all of the Lord of the Rings books. He is the reason why poor Frodo has to march into Mordor with Sam. Without Sauron's penchant for evil, there would be no story at all.
What's interesting is that, while he is the antagonist numero uno, we barely ever meet the dude. In fact, he doesn't appear in The Two Towers as a character, exactly. He is mostly the Enemy; all we know about him personally is that he lives (if it can be called living) in Barad-dûr, he has huge armies, and he wants to control all of Middle-earth. He is cruel and hateful, and he's very confident in his own abilities to take over the world.
While Sauron is the main Enemy of the whole series, Saruman is the particular antagonist of The Two Towers. It is his orcs that nearly carry off Merry and Pippin to Isengard, it is his armies that nearly destroy Helm's Deep, and it is his cruelty to trees that finally provokes the Ents to rise up in battle. The dude's a jerk.
By the end of The Two Towers, though, Saruman seems pretty thoroughly beaten. His walls have been torn down and his armies have been crushed. Even his palantír has gone into the hands of his enemies. But he is still alive, so we suspect that he has a lingering purpose still to come in The Return of the King.