Gandalf at the end says that members of Bilbo's family not yet born may one day understand the ring. And that the story is not really ending, but just beginning. These lines were not in the book, nor was there any indication that there was any more to the ring than mere invisibility. At the time the original book was written, there was no intention to connect The Hobbit with the Tolkien Legendrum which includes The Silmarillion and The Lord of The Rings (which hadn't been written yet). However, in 1977, it was well known that the ring Bilbo found and the events he participated in were a prelude to a much larger story.
The dwarves' map and runes upon it are an exact copy of the version included in the book, although the phrase indicated as written in the moon runes is incorrect. When Elrond holds the map of Lonely Mountain up to the moon and reads; "Stand by the grey stone when the thrush knocks and the setting sun will shine upon the keyhole," the runes shown actually read; "Five feet high the door, and three may walk abreast," the part of the map that was already visible, hence Gandalf's comment about the door being to small for Smaug to notice it.
In the book, Bilbo is knocked unconscious by a falling rock during the Battle of Five Armies immediately after seeing the eagles arrive to help. In the movie, perhaps due to an anti-war bias at the time of filming, Bilbo states that he "simply doesn't understand war" and then hides behind a stone, using the ring to become invisible and watching the entire battle. When asked about his whereabouts Bilbo lies and says that he had "a bump to the head" and was "out for hours".
John Stephenson, who voiced Bard (and others), was the original voice for Dr. Benton Quest in the original Jonny Quest (1964) cartoon series. After it was determined his voice was too similar to Mike Road's Race Bannon voice, he was replaced by Don Messick, who provides the voice for Balin (and others) here.
The Arkenstone, an heirloom of Thorin's dynasty and the most important treasure that he wishes to recover, isn't included in this film so neither is the surrounding storyline of Bilbo stealing the Arkenstone and giving it to the elves. This event causes noticeable friction between the two of them in the book which is explained in the movie as Thorin's irritation at Biblo's lack of understanding for war, something that doesn't happen at all in the book.
The only original song lyrics in the movie are those to "The Greatest Adventure" and other sections where that melody is used. All others are directly from the book as written by J.R.R. Tolkien or adaptations of what he wrote in verse form.
The song sung during the riddle game which ends giving the answer ("The answer is dark") is derived from one of the riddles Gollum asks in the book. All the riddles asked are directly quoted from the book, and there are five others not used.
The song sung while Bilbo and the dwarfs as they walk through Mirkwood, "Roads go ever ever on, Over rock and under tree, By caves where never sun has shown, By streams that never find the see," is taken directly from the book, although in it Bilbo sings it as he first sees Hobbitton upon his return.
The second song sung by the dwarfs at Bag End, "Far o'er the misty mountains cold, To dungeons deep and caverns old, We must away ere break of day, To seek the pale enchanted gold," is a direct quote of the first verse of the book version (which has ten verses).
The song sung as Bilbo frees the dwarfs from the elves by hiding them in empty wine barrels floated down the river ("Heave-ho! Splash plump! Rolling down the hole") is an adaptation of two songs from that incident in the book.
The song sung when Bilbo and the dwarfs arrive in Lake-town ("The streams shall run in gladness...") is the last verse of the song from the book. The final two lines (sung under the ensuing dialogue) are the first lines of the song.
The words sung after Bard and the Elvenking leave the mountain prior to the battle ("The dragon is withered...") are taken from a song in the book sung when Bilbo and Gandalf return to Rivendell on their way home.