Semiconductor nanowires provide promising low-dimensional systems for the study of quantum transport phenomena in combination with superconductivity. Here we investigate the competition between the Coulomb blockade effect, Andreev reflection, and quantum interference, in InAs and InP nanowires connected to aluminum-based superconducting electrodes. We compare three limiting cases depending on the tunnel coupling strength and the characteristic Coulomb interaction energy. For weak coupling and large charging energies, negative differential conductance is observed as a direct consequence of the BCS density of states in the leads. For intermediate coupling and charging energy smaller than the superconducting gap, the current-voltage characteristic is dominated by Andreev reflection and Coulomb blockade produces an effect only near zero bias. For almost ideal contact transparencies and negligible charging energies, we observe universal conductance fluctuations whose amplitude is enhanced because of Andreev reflection at the contacts.