Virginia De John Anderson's work considers the problems of animals in early English colonies. English settlers reversed traditional fencing practices. An abundance of land and shortage of labor meant that it was more practical to fence in crops and let animals forage freely for food. In practice, this meant that English livestock wandered through Indian hunting grounds and fields. (The environment was not a wilderness--people had carefully shaped it just as they had in the Old World.) Meadows were grazed down, Indian fields and crop stores were destroyed, and hogs rooted up coastal clams at low tide.

If the Galapagos becoming a stopover for ships counts in this, there have been issues there with invasive cats, rats, goats etc. Goats will eat just about anything that's a plant, so they can be damaging. Goats in the islands have been hunted to stop their environmental destruction.

I'd be interested to see answers regarding the mainlands though.