If you move as fast as superman you may be able to make yourself invisible, but for the ordinary person it is just not possible. Theories exist though that "prove" it is possible to make yourself invisible. Doctor Jensen Li and Professor John Pendry have written a paper which surmises making invisible paint.
Such material has to be extremely thin, having a structure smaller than the wavelength of visible light. Scientists have already made a small object invisible by cloaking it in a material comprised of tiny structures. If a material can be developed from nano-sized pieces it could be painted on an object and it would "bend" the light away from sight, i.e., the background would be visible.
Such a material has to be made from silica and silicon because variation in interpreting light is necessary. A person viewing a cloaked object would see a mirage of the background.
Don't be too hasty though - we are not in the Star Trek world yet. A person would experience only an illusion of the background!
Science