Yes, there are several examples of prejudicial exotic species. There is a tropical green algae (Caulerpa taxifolia, common in the aquarium trade) that is a real big problem in the Mediterranean (and now also California).
You may think that an alga is pretty harmless right, what can it do? Well, it is more successful than any native species and is driving all to extinction because it has no predators, so instead of a diverse array of algae, the Mediterranean will soon have only one species (which can't be eaten by the local fish and invertebrates because of its chemical defences).
There are also 20-30 marine fish that invaded the Mediterranean from the Red Sea via the Suez Canal, the problem with introduction of exoctic species is that you can never predict the outcome until it is too late.
Here is a link about the alga invasion if you want to read more:
Invasion of Caulerpa taxifolia
I kept my response to marine organisms, but there are several other examples of harmful introduction of exotic terrestrial species (they are easier to carry).