Based on data from real call centers, we develop, test, and compare forecasting methods to predict the waiting time of a call upon its arrival to the center, or more generally of a customer arriving to a service system. We are interested not only in estimating the expected waiting time, but also its probability distribution (or density), conditional on the current state of the system (e.g., the current time, queue sizes, set of agents at work, etc.). We do this in a multiskill setting, with different call types, agents with different sets of skills, and arbitrary rules for matching each calls to an agent. Our approach relies on advanced regression and automatic learning techniques such as spline regression, random forests, and artificial neural networks. We also explain how we select the input variables for the predictors.