It is known that the raw accelerometer data is combination of both linear acceleration and gravity. In order to isolate them w need to apply appropriate filters. I would like to know the real time applications where we would need only "gravity" or only "linear acceleration".
Gravity is used when you are trying to figure out the orientation of the phone. In other words, when you are trying to figure out how the user holds the phone. It is good for tilt games, for example you use the phone to drive a car, etc.
Linear acceleration is used when you are trying to figure out how the phone is shaken. It good for shaking games.
I highly recommend this video. In particular, between 4:15-6:10 and staring from 33:30 you see demos.