while taking a photo will create (in general) photos that most people will throw away the instant they see it. You can however exaggerate the moving part on purpose, and create some nice abstract photos (as shown below).
Note that you need to adjust the amount and direction of motion to the circumstances. Another important part is the shutter time in relation to how fast your moving / tilting the camera. This must be long enough to create the blurring part.
Just try it.