In my opinion, intrinsic motivation is the most important kind of motivation a person can have. Intrinsic motivation (motivation occurring with no obvious external consequences) causes people to feel more pride in the outcome. Of course the gain of a physical prize is always rewarding, the feeling is short lived. When something is achieved that is intrinsically motivated, the end reward is something to be proud of. Overall, intrinsically motivated behaviors, deliver more positive results and happier people.
One example of intrinsic motivation is the movie Forrest Gump. Forrest Gump is the story of a man with an extraordinary life accomplishing extraordinary goals with no intention of gaining any external stimuli. Here is a quick example of Forrest Gump's motivation!
One of the most important place to use intrinsic motivation is in the workplace. The video below discusses the negative effects of extrinsic motivation (bigger salary, more responsibilities, etc) and punishment (threatening). It makes the point that intrinsic motivation is key to having a successful workplace. When employees are working for a sense of autonomy, mastery, and purpose, their attitude towards work is much more positive than it would be if they were working towards a bonus.