In many optics applications, it is important to use well-polarized light. However, there are situations in which randomly polarized light has distinct advantages. We demonstrate two approaches by which a polarized light beam can be totally depolarized, each using a simple setup and inexpensive components. The first method, designed for narrow spectrum light, works by combining the horizontal polarization component of the beam with the delayed vertical component. The second method, which is most suitable for broad spectrum light, uses birefringent quartz plates. In both approaches, the polarization state is characterized by Stokes parameters measured using a rotating quarter-wave plate and fixed polarizer. We measure the coherence function of the electric fields and determine the minimum delay or quartz plate thickness required for decoherence. Coherences are modelled by Gaussian or Lorentzian functions and compared with the spectral properties of the light sources.