The voter model is a paradigm of ordering dynamics. At each time step, a random node is selected and copies the state of one of its neighbors. Traditionally, this state has been considered as a binary variable. Here, we address the case in which the number of states is a parameter that can assume any value, from 2 to 8, in the thermodynamic limit. We derive mean-field analytical expressions for the exit probability, the consensus time, and the number of different states as a function of time for the case of an arbitrary number of states. We finally perform a numerical study of the model in low-dimensional lattices, comparing the case of multiple states with the usual binary voter model. Our work sheds light on the role of the parameter accounting for the number of states.