Location data can be extremely useful to study commuting patterns and disruptions, as well as to predict real-time traffic volumes. At the same time, however, the fine-grained collection of user locations raises serious privacy concerns, as this can reveal sensitive information about the users, such as, life style, political and religious inclinations, or even identities. In this paper, we study the feasibility of crowd-sourced mobility analytics over aggregate location information: users periodically report their location, using a privacy-preserving aggregation protocol, so that the server can only recover aggregates -- i.e., how many, but not which, users are in a region at a given time. We experiment with real-world mobility datasets obtained from the Transport For London authority and the San Francisco Cabs network, and present a novel methodology based on time series modeling that is geared to forecast traffic volumes in regions of interest and to detect mobility anomalies in them. In the presence of anomalies, we also make enhanced traffic volume predictions by feeding our model with additional information from correlated regions. Finally, we present and evaluate a mobile app prototype, called Mobility Data Donors (MDD), in terms of computation, communication, and energy overhead, demonstrating the real-world deployability of our techniques.