There are many different types of cases for iPhones, or any smartphone for that matter. They range from hard shell cases to softer leather cases to screen protectors. I have found that the best case is simply a sock.
Although not a case, a sock serves the same purposes, protecting the device from damage. However, the sock case has a few distinct advantages. For one, it is very cheap. There is a high chance that you have lost one sock and therefore have an odd number of them. The sock case not only saves you money but also removes the inconvenience of having a sock without its pair. Second, the sock case while in your pocket actually cleans the screen of your device. The sock will remove fingerprints and such, making your device appear new every time you use it.
The sock case is not a perfect solution, however. Some disadvantages include the difficulty to remove your device from the case, the lack of protection when actually using the device, and the look you get when you pull your phone out of a dirty sock.