Longhorns and snakeheads and bees- Oh my

Over the weekend, I found a moment to peruse the Sant Ocean Hall online exhibit on the National Museum of Natural History website. I'm thinking ahead to some opportunities to get the little one to an exhibit that will catch his attention. I happened upon a page about the rapa whelk, a fairly recent exotic pest (some might say a menace) in the Chesapeake Bay region. It's been in various conservation groups' publications for a while.
What in the heck is a rapa whelk? It's a type of marine snail that has some nifty adaptations that allow it to spread itself around very quickly. Unfortunately, it's not from around here. It hails from Asia, almost certainly arrived in the bilge water of ships, preys on clams and oysters, and is a threat to the local marine snails. This presents yet another problem for the region's shellfish industry, not to mention the already badly degraded Chesapeake Bay ecology.
The rapa whelk is what's known as an invasive exotic species. This isn't a new idea. You've probably heard of many others, perhaps without realizing it: The fire ant, the Asian long-horned beetle, the gypsie moth, the zebra mussel, the European house sparrow, &c. This short list is merely the tip of the iceberg.
There are others that don't get peoples' hackles up, though: The honey bee, chickory, and the cattle egret, for instance. These pollinate many of our crops, make a proper cup of coffee for folks in New Orleans, and get rid of some of the fire ants that wouldn't have been here in the first place if we hadn't been so careless. (And, while we're at it, basically everything we eat comes from somewhere other than here.) These species are our friends, right?
I put some questions to the reader: Is it worth the effort to try to stop exotic species from invading new areas or to drive them out before they take hold? Is it appropriate to get rid of exotics that have been in an area for a long time? Does the usefulness or harm of the new species weigh on this? Should we hesitate to introduce an exotic crop? Should we simply accept that people will change the biosphere and make do with those changes?

Image source: Smithsonian Institution, National Museum of Natural History, Sant Ocean Hall