As a parent, and someone who attended a normal state school, with no alumni network, I never appreciated the resouces attached to strong alumni networks. However, now with a son at Stanford and a niece at Notre Dame I am shocked at how helpful it can be. If you have a choice between a school with a strong network and one that doesn't have one, there's only one way to go, with the alum.
Between my son and my niece we have discovered that the network is more like a brotherhood. Alumni truly go out of their way to help out others. Also in schools like ND and Stanford the alum are constantly coming to the school and recruiting, or looking to mentor etc etc etc......I know for a fact that my niece and son will do the same once they graduate. Its a real family environment in these types of schools.