The recently discovered superconductivity in MgB₂ has captured world attention due to its simple crystal structure and relatively high superconducting transition temperature T_c = 39 K. It appears to be generally accepted that it is phonon-mediated s-wave BCS-like superconductivity. Surprisingly, the strongly temperature-dependent anisotropy of the upper critical field, observed experimentally in magnesium diboride single crystals, is still lacking a consistent theoretical explanation. We propose a simple single-gap anisotropic s-wave order parameter in order to compare its implications with the predictions of a multi-gap isotropic s-wave model. The quasiparticle density of states, thermodynamic properties, NMR spin-lattice relaxation rate, optical conductivity, and H_c2 anisotropy have been analyzed within this anisotropic s-wave model. We show that the present model can capture many aspects of the unusual superconducting properties of the MgB₂ compound, though more experimental data appear to be necessary from single-crystal MgB₂.