Single rare gas atoms and polar molecules (water or ammonia) do not have an electron affinity because of their closed electronic shells. Yet, they have strong attractive polarization interactions with an excess electron. These attractions add up in large clusters and in the liquid, which thus can bind an excess electron. For our theory of negatively charged clusters we use a microscopic model of the polarization energy and include both initial and final state effects in the potential of the excess electron. We obtain that induced dipole moments partially screen the excess electron and the permanent dipole moments of polar molecules. This decreases the strength of the attractive polarization interaction and the electron affinity. Previous calculations of the electron affinity of clusters of polar molecules have used pair-potential approximations that neglect the screening. Thus the binding energy of the excess electron has been overestimated in comparison with the experiment. We also use our theory to study clusters of polar molecules containing an alkali metal atom because the valence electron separates from the metal atom and has the role of an excess electron. We present results for the electron affinity of clusters and liquids of various rare gases and of clusters of water and ammonia molecules. We obtain that the excess electron is delocalized in clusters of rare gas atoms and lies mainly outside the surface of the cluster except for very large clusters of krypton and xenon atoms, where it moves inside the surface. In contrast, for clusters of polar molecules the excess electron is localized at a small solvation center inside the cluster. We obtain a good agreement with experimental results for the binding energy of the excess electron. Our results for the vertical ionization potential of clusters of ammonia molecules and a metal atom suggest that a size-dependent transition from a single-center structure for small cluster sizes to a fully solvated two-center structure for large sizes is observed in experiments. For larger clusters of water molecules and a metal atom spherically symmetric model structures do not give any agreement with experiments. Our theory contains many-body polarization interactions. Thus it agrees well with macroscopic continuum models and with experiments. This theory also should be useful to examine the effect of solvents on the excitation spectra of molecules, on the dynamics of chemical reactions and on photosynthesis.