I cannot tell you how many times I've suggested to a client the idea of how we should design the interior of their closets and gotten in return odd looks and immediate questions of why. For reasons that are quite beyond me most people have taken to the notion that closet interiors should be white...simple, average white.
While there is always the option of putting a lot of design into a closet with custom woodwork, special organizers and the like doing something simple can be just as good. I personally love to wallpaper closets in wallpaper not used anywhere else in the house..except perhaps other closets. Painting a closet interior in a colour not used on other wall is a fast way to change your closets. Find a colour that really sets off your clothing and accessories and run with it, choose a colour that suits your personality, your lifestyle.
Since it is a small space that isn't seen that often I even suggest picking a paint colour you have always been afraid to use anywhere else. Mirror the entire interior, cover it in cork, upholster it, the sky (or little enclosed space) is the limit. Use this space to experiment with ideas you might want to use in bigger public spaces.