Unfortunately, a number of ornamental fish have become invasive species in various areas of the world. This means that they are living and breeding successfully in areas where their species did not evolve. Species that have become invasive include guppies, gambusia, white cloud mountain minnows, swordtails, walking catfish, goldfish, and oscars. In some cases, invasive species have caused native species to go extinct. A classic example is the Nile Perch, Lates niloticus, which caused the extinction of over two hundred Cichlid species when it was introduced to lake Victoria (Global Invasive Species Database), although this fish was introduced intentionally as a food fish, rather than as an escapee from home aquaria.  The guppy, Poecilia reticulata, is a common aquarium fish that is believed to have played a role in the decline of several threatened species, and to be a carrier of exotic parasites (Global Invasive Species Database).

Hotsprings in cold areas that contain endemic species are especially vulnerable to invasion because any species already present are present only in a small area where they can easily be overrun by an aggressive species imported from elsewhere. Also vulnerable are island species, endemic lake species and others with small natural habitats.  These are vulnerable for the same reasons as hot springs. Species whose habitat has been disturbed are also vulnerable. Habitat disturbance often occurs along with invasive species problems, since the already changed ecosystem is likely to provide opportunities for invasive species that arrive in the area and many of the native species are stressed by the changes that have occurred in their natural habitat.

This is the main reason why it is important not to release ornamental fish into the wild. There are also a couple of other reasons. If the environment is unsuitable for your fish, they will die. This is cruel to your fish. There is also the possibility of them introducing exotic diseases which transfer to native species.

References:

Global Invasive Species Database               http://www.issg.org/database/species/ecology.asp?si=89