A rigorous mode matching technique combined with Floquet's theorem is applied to analyze a variety of periodically loaded dielectric waveguides. Characteristic equations of the structures are derived. Dispersion relations and the phase/group velocities are determined by solving the characteristic equations. Numerical results including the passband/stopband characteristics, slowing down of phase velocities, and a backward wave phenomenon are presented. The dependence of the dispersion curves on the structures' parameters is discussed. Properties of complex modes existing in the prohibited frequency bands are also explored. These structures have potential applications in microwave and millimeter wave filter networks and slow wave or backward wave structures for traveling wave tubes devices.