We report and characterize anomalous orbital-energy changes observed during six Earth flybys by the Galileo, NEAR, Cassini, Rosetta, and MESSENGER spacecraft. These anomalous energy changes are consistent with an empirical prediction formula which is proportional to the total orbital energy per unit mass and which involves the incoming and outgoing geocentric latitudes of the asymptotic spacecraft velocity vectors. We use this formula to predict a potentially detectable flyby velocity increase of less than 1 mm/s for a second Rosetta flyby on November 13, 2007.