It is a common myth that sunflowers move all day long. Many believe that the flowers track the movement of the sun and move along with it.
When sunflowers are in their very early budding stages, they typically turn to face an easterly direction through a process called "heliotropism". However, they do not continue to change directions as they grow older and the flower forms.
The myth of the sunflowers moving to follow the sun throughout the day more than likely came about because when you see a field of sunflowers, they are all facing the same direction. It is indeed a beautiful sight to see.
So if you are ever lost without a compass, look for a field of sunflowers and follow them east.
A very cool (but fake) video is at http://www.youtube.com/watch?v=g8mr0R3ibPU It is nice to watch with birds chirping and bees buzzing!