Photonic crystals (PCs) made of anisotropic dielectric materials support electromagnetic waves of coupled polarization. This wave-coupling property can be used in the design of important optical devices. We demonstrate that a one-dimensional structure composed of anisotropic dielectric materials can be used to design a transverse-electric/transverse-magnetic polarization converter. The major benefit of this converter is the combination of an identical and very high polarization conversion efficiency for both reflection and transmission waves. Furthermore, we investigate the fact that for an appropriate choice of material and geometrical properties, the birefringent photonic crystal can exhibit an absolute photonic band gap (PBG) in which light propagation is forbidden for all polarizations and for a given plane of incidence. We also explore the possibility of exploiting a single-defect anisotropic photonic crystal to fabricate an optical switch and a selective electromagnetic filter. In these optical devices, the birefringence of the photonic crystal layers increases the performance of the optical device compared with the isotropic structure.