The role of unbiased migration in cooperation was explored based on the stady of spatial evolutionary game in the framework of a variety of spatial structures, including regular lattice, continuous plane and complex network. A striking finding is that migration plays a universal role in cooperation, regardless of the kind of spatial structures. For high degree of migration, cooperators cannot survive due to the failure of forming cooperator clusters to resist attacks from defectors. While for low degree of migration, cooperation is considerably enhanced compared with that in statically spatial game, which is due to the strengthening of boundary of cooperator clusters by the occasionally accumulation of cooperators along the boundary. The cooperator cluster thus becomes more robust than that in static game and defectors nearby the boundary may be assimilated by cooperators, so the cooperator cluster expands, which facilitates cooperation. The general role of migration can be substantiated by sufficient simulations associated with heuristic explanations. An aspirationinduced migration was proposed which individuals will migrate to new sites provided that their payoffs are below some aspiration level. It is found that moderate aspiration level can best favor cooperative behavior. In particular, moderate aspiration level enables cooperator clusters to maintain and expand whereas induces defector clusters to disintegrate, thus promotes the diffusion of cooperation among population.The results provide insights into understanding the role played by migration in the emergence of cooperative behavior.