In this study, realization and applications of anisotropic zero-refractive-index materials are proposed by exposing the unit cells of photonic crystals that exhibit Dirac-like cone dispersion to rotational symmetry reduction. Accidental degeneracy of two Bloch modes in the Brillouin zone center of two-dimensional C-2-symmetric photonic crystals gives rise to the semi-Dirac cone dispersion. The proposed C-2-symmetric photonic crystals behave as epsilon-and-mu-near-zero materials (epsilon(eff) approximate to 0,mu(eff) approximate to 0) along one propagation direction, but behave as epsilon-near-zero material (epsilon(eff) approximate to 0, mu(eff )not equal 0) for the perpendicular direction at semi--Dirac frequency. By extracting the effective medium parameters of the proposed C-4- and C-2-symmetric periodic media that exhibit Dirac-like and semi-Dirac cone dispersions, intrinsic differences between isotropic and anisotropic materials are investigated. Furthermore, advantages of utilizing semi-Dirac cone materials instead of Dirac-like cone materials in photonic applications are demonstrated in both frequency and time domains. By using anisotropic transmission behavior of the semi--Dirac materials, photonic application concepts such as beam deflectors, beam splitters, and light focusing are proposed. Furthermore, to the best of our knowledge, semi--Dirac cone dispersion is also experimentally demonstrated for the first time by including negative, zero, and positive refraction states of the given material.