Here we present the results of our theoretical analysis for guided modes in parallel-plate waveguides filled with pairs of parallel layers made of any two of the following materials: 1) a material with negative real permittivity, but positive real permeability (epsilon-negative); 2) a material with negative real permeability, but positive real permittivity (mu-negative); 3) a material with both negative real permittivity and permeability (double-negative); and 4) a conventional material with both positive real permittivity and permeability (double-positive) in a given range of frequency. Salient properties of these guided modes are studied in terms of how these materials and their parameters are chosen to be paired, and are then compared and contrasted with those of the guided modes in conventional waveguides. Special features such as monomodality in thick waveguides and presence of TE modes with no-cutoff thickness in thin parallel-plate waveguides are highlighted and discussed. Physical insights and intuitive justifications for the mathematical findings are also presented.