A lot of the European ones have been here so long people don't really call them invasive but they still are. Some common ones like honeybees, wild horses, pigs (boar), rats, mice, feral cats.
> The appeal of acclimatisation societies in colonies, particularly Australia and New Zealand,[12] was the belief that the local fauna was in some way deficient or impoverished. There was also an element of nostalgia in the desire of European colonists to see familiar species.[13] An Australian settler, J. Martin, complained in 1830 that the "trees retained their leaves and shed their bark instead, the swans were black, the eagles white, the bees were stingless, some mammals had pockets, others laid eggs, it was warmest on the hills..." It was there that the desire to make the land feel more like England was strongest.
> Eugene Schieffelin ... became chairman of the American Acclimatization Society and joined their efforts to introduce non-native species to North America for economic and cultural reasons. His 1890 release of European starlings in Central Park resulted in the first successful starling nesting in North America to be observed by naturalists.
> In 1864 the commissioners of Central Park had introduced Java sparrows, house sparrows, chaffinches and blackbirds into the park. The European sparrows were reported to have "multiplied amazingly". They quickly became one of the most common birds in New York, though the others did not seem to do as well. After the society's founding, such efforts were redoubled. The group's annual meeting held at the Great New York Aquarium in 1877[4] reported that the release of 50 pairs of English skylarks into Central Park had only been a partial success, since most had flown across the East River to take up residence at Newtown and Canarsie in Brooklyn. At the meeting, the recent release of European starlings, Japanese finches and pheasants into the park were noted. The meeting adjourned with the group resolved to introduce more chaffinches, skylarks, European robins and tits—"birds which were useful to the farmer and contributed to the beauty of the groves and fields"—in the city.[5]