Very good question.....
I consider "trash fish" to be any fish that gets out of hand to the point that the NGPC or the DNR has to kill of the lake and start over again. Examples of this are/were the stunted yellow/white bass at Cunningham, yellow bass and carp at Anita and 12-Mile, and carp at Icaria. However in areas that "trout is king" I've heard of lakes being killed off because of too many Northern Pike.

They are by no means trash fish in my book!
I guess it's just a matter of opinion. I love to catch carp, and gar, but I'd rather keep them out of a lake if it meant catching bigger and more bass and catfish!