The slip-stick phenomenon is present all around us, be it the noise of car breaks or in earthquakes. But does it have any real-life application?
Another application is the frictional force spectroscopy in the stick slip mode. There you use an AFM (atomic force microscope) and you move it laterally over the surface (Actually I think you move the sample, but it doesn't matter). You are performing this so slowly that the cantileaver sticks and slips. From these kinds of measurements you can determine the dissipated energy. See the wikipedia article for AFM for further informations or this article http://en.wikipedia.org/wiki/Chemical_force_microscopy#Frictional_force_mapping
Yes, grasshoppers use it to create the sounds they use for attracting mates.
Actually I don't know of any applications other than generating sounds. As Calmarius mentions in the comment, stringed instruments played with a bow use stick-slip motion to make the string vibrate. In the old days teachers used it to make excruciating noises with chalk on the blackboard.