On the left here is a follow move. The motivation here is obviously the action. Camera moves such as this help bring excitement into the film. Imagine seeing a car chase where the camera stays still. Seeing the cars race in and out of the scene isn't as exciting as having the camera travel along with the cars. This helps bring the audience into the film. It also helps clarify some of the action. These types of moves are especially helpful if you have dialog or particular acting you want the audience to see while the action is taking place. Again speed is a crucial part of these moves so the action feels natural to the characters.
Other types of moves that help convey particular moods is truck in's and out's during dialog lines. Moving in can help give the feeling of concern or surprise. Moving out can give a feeling of loneliness or being overwhelmed. And remember just because the camera is moving doesn't mean a character can't move into or out of the scene ahead of the speed of the camera.
These days I often see storyboard artists using camera moves to compensate for their inability to make a good composition or to keep a drawing of a character inside the field. This usually results in a camera adjustment which is completely unmotivated. Make sure your camera moves are well planned and the audience will generally be unaware the camera is moving. Just because you are working on a 3D film doesn't mean the camera has to keep moving all the time. Don't let camera moves lose your audience.