We examine inducing the self-gravitational collapse of molecular cloud cores with stellar ejecta. We study the effect of winds of various strengths arriving at cloud cores modeled as marginally stable Bonnor-Ebert spheres, which are unstable both to collapse and to expansion. We find that some winds instigate collapse of the cloud core, while others result in expansion or destruction of the cloud. Collapse occurs when the incident momentum of the ejecta is greater than approximately 0.1 MMsun0 km s-1 for the standard γ = 1 wind and 1 Msun cloud scenario. The critical momentum, which divides those cases which induce collapse and those which do not, scales as the mass of the cloud times its sound speed, which is 0.2 MMsun0 km s-1 for the standard to K cloud. The critical momentum is exceeded for some supernova and many protostellar outflows, although if the wind has a velocity greater than approximately 100 km s-1, the effective adiabatic index will be γ = 5/3 and the cloud will be destroyed, through shredding into many pieces. The planetary nebulae of AGB stars appear to have momenta below the critical value. However, we found that a high wind temperature (T ∼600 K), possibly characteristic of AGB star winds, could instigate collapse even in low momentum winds.