I liked the movie, so I grabbed the book from the UNH library.
The main thing I noticed—probably so much so that it interfered with taking the book on its own merits—was how much major surgery on the plot and characters was involved for the movie.
In both book and movie, the basic premise is that people have long-since stopped having babies, for reasons nobody knows. This causes increasing social dysfunction and political tyranny. Things change when (also inexplicably) a young woman becomes pregnant; everyone wants to use her for their own purposes. Theo, the protagonist, becomes the protector of the woman and they undertake a long-odds journey to ensure the baby's safety.
But just about everything else is different. Movie-Theo is a bureaucrat and a drunk; book-Theo is a college literature professor. Both had a child whose death precipitated the breakup of his marriage, but in the movie the child just got sick; in the book, it's a car accident caused by Theo. Book-Theo just happens to be the cousin of the "Warden", the dictator in charge; Movie-Theo's ex-wife just happens to be the leader of a group of rebels.
These and a host of other changes change everything on motivational and character levels.
Ross Douthat thought the book much superior to the movie; I think both are fine on their own terms. If anything, I think both understate the kind of chaos that would actually occur if there were no more children born.
Update: I was impressed by the movie/book differences, but you might want to check out Mark Steyn, who was dismayed by them.
Another update: they are, for some reason, all over this book-vs-movie thing at The Corner today, with a lot of links. If you're interested: here; here; here; here; here. After reading those links, I'm reminded that I'm a superficial Philistine.