Early in the novels, Frodo Baggins and his hobbit friends encounter Tom Bombadil, a "master of the woods" who lends them aid. Bombadil does not appear in the movies.
The elf princess Arwen (played by Liv Tyler in the movie) appears only briefly in the books. She plays a much larger role in the movies, most notably by spiriting Frodo (played by Elijah Wood) to the ford at Rivendell.
Narsil is the broken sword reforged in "Return of the King." In the books, Aragorn carries the pieces with him; in the movies, it is on display at Rivendell.
The battle of Helm's Deep in the movies contains a number of departures from the book, notably the arrival of the elves to help and the presence of Eowyn (played by Miranda Otto) at the fortress.
Towards the end of the books, Frodo, Sam, Pippen and Merry must stop Saruman and Grima Wormtongue, who have taken over the Shire in their absence. The sequence was completely omitted from the movies.