The House Sparrow was introduced to North America from Europe. It is not really a sparrow but a European weaver-finch. It is highly successful, tends to follow human habitation, thrives in agricultural areas, and does not damage the local ecosystem. I would rate it a neutral. Bird of the Day: A Sparrow that's not a Sparrow, and a Successful Immigrant
The reintroduction of wolves into Yellowstone has had a positive effect on the ecosystem there. Wolf Reintroduction Changes Ecosystem
Horses were also introduced from Europe to North America and seem to have been neutral toward the ecosystem (unless you are a cattle rancher). They could be considered a reintroduction since they did evolve in North America also but just died out in the past.
Wild turkeys were introduced to the Western states from its native location in the Eastern US. They have been successful and effect on the ecosystem seems at worst neutral.
Two introductions that we regard as very beneficial animals, the earthworm and the European honeybee had negative effects on the native North American ecosystem, but very positive effects on those plants that the settling Europeans were trying to grow. The earthworm had been killed off the ice age in the Northeast and was introduced via the ballast from ships. Earthworms ground through leaf litter that the trees depended on and resulted in sparser forests. Honeybees were deliberate introductions. The native bees were few and favored only a few plants. The European honeybee was enormously fertile and liked pretty much all flowering plants making it a major league pollinator. My source for this information earthworms and honeybees is America, Found and Lost