We always hear about invasive species that reek havoc on an ecosystem or the environment, but are there times when a new species has been introduced and has actually been mostly positive.
Horses. When Spain brought horses to the new world the plains tribes adapted to them in a positive manner. I don’t believe they harmed the environment in a significant way at the time (or now). The pigs they brought over are another matter.
Going the other way I believe the potatoes, tomatoes, bananas, maize, cacao, sunflower, and squash were sent back to the old world and adapted in a positive way.
The honeybee is an introduced species to North America. It has overall been very beneficial and we’re very afraid of losing the species. There is a decent chance they did damage back in the 1500s but I don’t know of it.
Horses were just reintroduced into their native range after a brief absence.
Earthworms are an invasive species to much of North America, native earthworms having been almost completely wiped out during the Ice Age.
However, though they were once thought to be generally beneficial, or at least benign to the environment, it’s now believed that they may be a slow-motion threat to the ecosystem.
Apples, I suppose. Crab apples are native to North America but are useless as a food product, but the foreign apple trees we imported here don’t seem to have done much damage. And of course, they’ve provided a net benefit in terms of food and (for a time, then forgotten about for a century, and then came back) alcoholic beverages.
I live near the oldest distillery in the USA. It never stopped making Apple Jack except during prohibition. Most apple growing places kept up the tradition of hard apple cider. It just wasn’t a bar drink for that century I guess.
Striped Bass in CA. Generally the introduction of the Largemouth Bass is heralded as successful.
And brook and brown trout in many streams and lakes, but they have competed with the endangered California golden trout.
There are quite a few introduced/invasive fish species in CA:
https://calfish.ucdavis.edu/Non-Native_Fish_Species/
This is kind of my point. Not too many time something new is introduced and it works out for the betterment.
Aren’t Eucalyptus trees from Australia. I’ve never heard of them being an issue, but I guess plants are less invasive than animals.
Yes, and yeah, the various CA parks etc are phasing them out. In the Park where I was a ranger, all new growth was cut down, but the old trees were left, unless they got diseased or something.
Honeysuckle, kudzu, dandelions, tumbleweed, English ivy, and poison hemlock would like to have a word with you.
The dung beetle - a deliberately introduced animal, as opposed to invasive by accident.
When I was a kid every summer meant millions and millions of flies because of the vast amounts of cattle and sheep shit produced in Australia. The dung beetle was introduced in a systematic project from 1968 to get it all biologically managed. Now flies are pretty inconsequential in summer - I’m happy, they’re happy.
The question here is always going to be, beneficial to whom? Or to what? Earthworms are good for farms, but bad for forests: Is that a win or a loss? Those Australian dung beetles are bad for the flies, but good for anyone who doesn’t like flies. Or consider the sheep that made the dung beetles necessary: I’m sure the shepherds consider them beneficial, but other parts of the ecosystem might disagree.
Add peppers to the list. And coffee in the other direction.
Perhaps the most prominent example would be to ask whether humans should have stayed in Africa.
“Many were increasingly of the opinion that they’d all made a big mistake in coming down from the trees in the first place.”
A good book to read on the subject is Mann’s 1493: Uncovering the New World Columbus Created (follow-up to 1491 ) which covers a lot of the changes brought by the discovery of the Americas and the effects on commerce, agriculture, health, ecology etc. of the transfer of assorted species between old and new worlds.
I seem to recall that camels were introduced to the Middle East somewhat after biblical times - and seem to have become indispensable since then. But that would go for almost every agricultural species, I assume.
Buffalo might disagree 
Transplants are not the same as invasives. I don’t know if any of those have gotten into the wild in any significant way.
They’re a huge issue here.
Here as well, though admittedly there is no unanimity on it.
I think for something to even have a chance of being ‘wholly beneficial’, it would have to be introduced to a completely unexploited niche where there is no existing biology to mess up. Such a scenario feels like it might be something of a rarity in nature.