In the afterglows of several gamma-ray bursts (GRBs), rapid temporal decay, which is inconsistent with spherical (isotropic) blast-wave models, is observed. In particular, GRB 980519 had the most rapidly fading of the well-documented GRB afterglows, with t-2.05+/-0.04 in optical as well as in X-rays. We show that such temporal decay is more consistent with the evolution of a jet after it slows down and spreads laterally, for which t-p decay is expected (where p is the index of the electron energy distribution). Such a beaming model would relax the energy requirements on some of the more extreme GRBs by a factor of several hundred. It is likely that a large fraction of the weak- (or no-) afterglow observations are also due to the common occurrence of beaming in GRBs and that their jets have already transitioned to the spreading phase before the first afterglow observations were made. With this interpretation, a universal value of p≅2.4 is consistent with all data.