@Whyonearth: Forget these people telling you that you don't know how to pocket your own phone properly. Or the even more unhelpful people who throw the Apple warranty conditions in your face.
I too have an iPhone 5c and a few shallow scratches have begun to appear. Good news is that there are several ways to get rid of them. You will need a polishing cloth and either a can of Brasso (believe it or not) or that scratch removal cream used for cleaning glass stove tops. Another cream product is www.radtech.us/products/icecreme which is allegedly made for the iPhone, but I've never tried it before.
Just put a small amount of Brasso or the cream on the polishing cloth, then lightly rub the iPhone plastic in circular motions, applying a moderate amount of pressure only. Give it a minute to dry, then buff out the residue using a clean part of the polishing cloth. Repeat this a few times and your scratches will be mostly gone and your 5c backing will be shiny again too.
I learned this trick a few months ago when I researched how to bring the red plastic handles on my Swiss Army knife back to near-new condition. It works. I don't see why I should have to use a case to protect my iPhone when all Apple talks about is the research and development they put into their 'space age' materials. Besides which, what's the point of owning a nice thin phone if you're just going to cover it up with a thick, ugly case? I don't mind having to polish my 5c every once in a while.