The ability to slow down light leads to strong light-matter interaction, which is important for a number of optical applications such as sensing, nonlinear optics, and optical pulse manipulation. Here, we show that a dramatic reduction in the speed of light can be realized through the interference of electric and magnetic dipole resonances in Mie-type resonators made of a dielectric material with a high refractive index. We present a general theory that links the maximal speed reduction of light to resonator radiation losses and then consider a specific realization based on silicon nanodisk arrays.