"I cannot wait to go home and pawn this."
The Book: Bilbo awakens in total darkness; it's so dark he literally cannot tell the difference between having his eyes open or closed. He gropes around on all fours, and his hand accidentally brushes against a small ring of cold metal. He puts it in his pocket without thinking and continues on his way. He sits down for a moment. He feels for his pipe, then for his tobacco, but cannot find a match. That's the last straw for Bilbo Baggins' hopes, and he despairs for a moment. He draws his sword, and noticing that it "shone pale and dim before his eyes," found enough hope to continue. Using his sword as a source of light, he trots along.
What difference does it make? This is actually a pretty big difference. In the book, Bilbo just tosses the ring in his pocket while he's freaking out in the dark, and never gives it a second thought until the game of riddles (I'll discuss how this actually affects that game later). He doesn't know that it belongs to Gollum, that it's made of gold, or anything about it. In the movie, he deliberately steals a precious object from an unhinged cave-dweller, after stopping to give it a close look.
My Opinion: I do like this change, honestly, though there is both good and bad to it. The book keeps Bilbo's morality and good character intact by having him pocket an object he finds abandoned in some cave without a second thought. He forgets he even has it until he puts his hand in his pocket later. In the movie, he sees that it belongs to somebody, but still takes it. Furthermore, it's so incredibly unlikely for Bilbo to have found the ring in the book - it almost makes it look like he found it by some force of fate, as if the ring wanted to be found.
However, both problems can be easily explained in the framework of the movie. If the ring did indeed want a new owner, then having it "luckily" fall out of Gollum's pocket at the right moment serves the exact same purpose as having Bilbo stumble upon it by blind luck. Furthermore, Bilbo Baggins is a burglar. Having him steal things is pretty much par for course. It's all honestly worth it, in my opinion, to answer the question I've had for so long: if Gollum loves the ring so much, why would he keep it in a pile of garbage in his little hut? How can he go so long without noticing its missing? The movie, at least, provides an answer.