Directional light scattering by spherical silicon nanoparticles in the visible spectral range is experimentally demonstrated for the first time. These unique optical properties arise because of simultaneous excitation and mutual interference of magnetic and electric dipole resonances inside a single nanosphere. Such behaviour is similar to Kerker's-type scattering by hypothetic magneto-dielectric particles predicted theoretically three decades ago. Here we show that directivity of the far-field radiation pattern of single silicon spheres can be strongly dependent on the light wavelength and the nanoparticle size. For nanoparticles with sizes ranging from 100 to 200 nm, forward-to-backward scattering ratio above six can be experimentally obtained, making them similar to 'Huygens' sources. Unique optical properties of silicon nanoparticles make them promising for design of novel low-loss visible- and telecom-range metamaterials and nanoantenna devices.