Use fragments when you are writing dialogue to convey terseness and efficiency with words. This also makes dialogue more realistic because people, in general, speak in sentence fragments. "Pie! For me?" is a good example because it uses two sentence fragments to show the person's excitement.
Use a sentence fragment to highlight a point. For example, you could write: "I had just gotten the biggest contract of my life. Not of the week. Of my life." These two sentence fragments emphasize how important the contract is because they show the writer's desperation to get the information out.
Write with sentence fragments to "trick" the reader with a juxtaposition. This is a good use of sentence fragments because it catches the reader off-guard, as he doesn't have the time it takes to read and process an entire sentence. So, you could write: "The box had all the tools of the trade. It had hammers, nails, drills and screwdrivers. Alongside a pile of onions."
Make sure you don't use any accidental sentence fragments as these will make your purposeful sentence fragments look like grammatical mistakes rather than writing devices. A case in point: "An example of an. Accidental sentence fragment" undermines your purposeful sentence fragments.