In Jared Diamond’s book, Collapse, one of the case studies he examines is the introduction of, I believe, rabbits to Australia. They were brought in for game hunting, and actually the first attempt failed so people tried again. However, they soon bred out of control and now the ecosystem there is devestated.
This is kind of the opposite – feral cats were identified as having a deleterious impact on the environment, so they got rid of them, but now some other “immigrant” species is running amok.
I think it says a lot about how sensitive ecosystems are, especially ones that have been largely isolated for so long such as those around New Zealand and even Australia.