I'm just reading it now, but I haven't finished, so this won't exactly be a complete list.
- Bilbo found the ring in the Goblin caves in the Misty Mountains, and it was in complete darkness, so he had not even known what he had picked up or what magical qualities it had.
- Beorn isn't in his bear form when the Dwarves show up, nor is he chasing them. Gandalf led the group to his house, and then made them arrive every five minutes in groups of two as he told their story of how they ended up on that side of the Misty Mountains - with Bombur coming last as he would suffice for two.
- Legolas and Tauriel never show up; in the book, it's Bilbo who fights and manipulates all the giant spiders. He also names his dagger/sword "Sting" when the spiders think that it is a stinger on the side of his body, not because it stings when they get stabbed by it.
- When the Dwarves escaped their encapturement by the Elves, there were no orcs/goblins chasing after them
- Fili and Kili are supposed to have large beards, and are also supposed to have lighter hair, as described in the very beginning of the book. Fili only loses his beard after he was captured by the spiders and had to cut it off because of the spider web tangled in it.
As I said before, I have not quite finished the book, so I don't know of any other possible differences, but these are some that came to mind right away.