Many applications such as recommender systems (RecSys) are built upon streams of events, each associated with a type in a large-cardinality set and a timestamp in the continuous domain. To date, most applied work is focused on the prediction of the type of the next event, i.e., which exact item a user may visit when they arrive at the RecSys. Instead, we aim to predict when and how often an event of a certain type will be visited by the given user, without the implicit assumption that they will arrive and consume exactly one item at a time. This perspective leads to unique applications in user recommendation (UserRec), where the RecSys is tasked to preemptively match users on behalf of the item producers for marketing purposes. We propose Recurrent Intensity Models (RIMs) that incorporate user visitation intensities in the RecSys, based on recent progress in temporal processes. To our knowledge, our work is the first to approach UserRec completely based on hidden temporal representations without heuristics from explicit feature engineering.