Even the Nazgul were just puppets and extensions of his power. His underlings were not fond of him at all and served him far more out of fear than out of either respect or loyalty.
The theatrical versions were lengthy epics (all clocking around at 3-ish hours), and the "Extended Editions" (released before the succeeding movies) added at least another half-hour to each film's running time.
Among the most significant changes include Saruman's last scene, the characterizations of Aragorn, Gimli, Faramir, Denethor, and Arwen, as well as the removal of various subplots to make the story as a whole more appealing to movie audiences or to streamline their remarkably nuanced events from the books. The films were remarkably faithful in many respects, though many changes had to be made due to the many factors involved with adapting such a monumental work.