The interaction of a stellar or disk wind with a collapsing environment holds promise for explaining a variety of outflow phenomena observed around young stars. In this paper we present the first simulations of these interactions. The focus here is on exploring how ram pressure balance between wind and ambient gas and postshock cooling affects the shape of the resulting outflows. In our models we explore the role of ram pressure and cooling by holding the wind speed constant and adjusting the ratio of the inflow mass flux to the wind mass flux (_a/_w) Assuming nonspherical cloud collapse, we find that relatively strong winds can carve out wide, conical outflow cavities and that relatively weak winds can be strongly collimated into jetlike structures. If the winds become weak enough, they can be cut off entirely by the infalling environment. We identify discrepancies between results from standard snowplow models and those presented here that have important implications for molecular outflows. We also present mass versus velocity curves for comparison with observations.