The iPhone has a special layer that protects against grease spots. This layer is called an oleophobic coating. It now seems to wear off when used in intensive ways. A user reports that after intensive use of the game Flick Fishing, a circular spot appeared on the screen. With Flick Fishing you have to make the same circular motion over and over, to catch a fish. The special projecting layer is meant to make it possible to erase finger stains more easily. The stains are still visible but can be erased by just wiping them of with as much as a single wave of a piece of cloth. » Oleophobic Screen Wearing Off