The magnetic, transport, and optical properties of EuFe₂ As₂ single crystals have been investigated parallel and perpendicular to the ab plane. The anisotropy ρc / ρab 8 depends only slightly on temperature. In both orientations, the spin-density-wave transition at T_SDW =189 K shows up as a considerable increase in the dc resistivity. Susceptibility measurements evidence the magnetic order of the Eu²⁺ moments at T_N =19 K with little influence on the electronic transport taking place in the FeAs layers. Polarization-dependent infrared spectroscopy reveals strongly anisotropic optical properties and yields a carrier density of only 4.2× 10²¹ cm^-3 and a bandmass of mb =2_m0. A sizeable Drude contribution is present at all temperatures and narrows upon cooling. Below T_SDW, the spin-density-wave gap develops in the in-plane optical conductivity; no appreciable change is detected for the perpendicular polarization. Modifications in the phonon features are associated with changes in the electronic properties at T_SDW. The extended Drude analysis yields a linear behavior of the frequency-dependent scattering rate below T_SDW, indicating an interaction between the charge carriers and spin fluctuations in the spin-density-wave state.