We study correlations in temporal networks and introduce the notion of betweenness preference. It allows us to quantify to what extent paths, existing in time-aggregated representations of temporal networks, are actually realizable based on the sequence of interactions. We show that betweenness preference is present in empirical temporal network data and that it influences the length of the shortest time-respecting paths. Using four different data sets, we further argue that neglecting betweenness preference leads to wrong conclusions about dynamical processes on temporal networks.