Frodo is motivated primarily by necessity, having been granted visions of what will happen to the world should be fail, he is willing to sacrifice whatever he must to accomplish his job. However, by the end of the story, he has no resources left to go on or to resist the Ring, and it falls to Sam to carry through much of the last parts of the journey. In fact even before that, Frodo has entered a state of virtuous apathy- a detachment from the costs of his burden that allows him to continue when he wouldn't otherwise be able to. For more thoughts on apathy as a virtue, please visit my Writing section.
Frodo is granted a place in the Undying Lands for his part in the defeat of Sauron, and honor unmatched by any Hobbit before or since.
