Beginning with the γ-ray bursts GRB 970228 and GRB 970508, a standard model for the interpretation of gamma-ray burst (GRB) afterglows emerged involving synchrotron emission from a constant-energy blast wave expanding into a constant-density, "interstellar" medium. However, a massive star origin for GRBs implies a stellar wind environment, probably a Wolf-Rayet star, and we have previously suggested wind interaction models for the afterglows of GRBs 980326, 980519, and 980425/SN 1998bw. Here, we extend the theory of afterglows in winds, considering strong cooling phases, the transition to nonrelativistic motion, jets, and prompt reverse-shock emission. We find that, compared to the interstellar case, the optical prompt emission in the wind case could have a comparable magnitude but would die off faster. We examine the afterglows of other well-observed GRBs in the context of wind interaction models and find that GRBs 970228 and 970508 are likely wind interactors. The revision in the nonthermal afterglow emission from GRB 970228 caused by the recognition of late supernova emission favors wind interaction. The radio evolution of GRB 970508 provides especially strong evidence for wind interaction. For GRB 970508, the observations suggest a density that is compatible with that expected in a Wolf-Rayet star wind. Finally, observations of the afterglow evolution of GRBs 990123 and 990510 and the prompt optical emission from GRB 990123 favor interstellar interaction models, which would suggest compact star merger progenitors for these objects.