Here’s a pretty cool conceptual idea for a cell phone powered by kinetic energy. The Atlas Kiinetic Cell Phone has a mechanism in the center behind some glass that you can actually see work. As you move the phone around, a weighted piece rotates around to wind up a spring which powers the phone.
According to the designer, only a few times of turning the phone upside down and back will power it up. This same kinetic type of mechanism works great to power watches and is actually not that uncommon. The only difference is that watches for the most part need very little power to run compared to a phone.