I am pretty much exclusively a saltwater fisherman, but I have a garden pond in my backyard I keep stocked with native fishes - sunfishes and gambusia mostly. I use a cast net to catch the fish in nearby creeks and bayous. Yesterday I caught a tilapia in my net. It led me to wonder - if such an infrequent freshwater fisherman as myself is catching a tilapa, how often are frequent freshwater anglers catching nonnative fishes in their waters?
So what have you caught?
Brown Trout, Carp, Striped Bass in
California, Florida Strain Largemouth Bass in California, Kamloop and Eagle Lake strains of Rainbow trout outside their native waters, Walleye in South Carolina Lakes, etc…
FY
Hmmm
Here the waters stay warm enough in the winter that we’ve got some established populations of some of the hardier tropical fish released by irresponsible aquarium owners - tilapia, plecostomus catfish, Texas cichlids (which are only native in the extreme southern part of the state), even jack dempsey cichlids and convict cichlids.
My favorite species isn’t a native fish
Smallmouth bass are my favorite quarry in my home waters, but it isn’t native to here. I’m not sure if that makes it an exotic the way you described above, but I think it meets your definition.
There actually aren’t many sport fish that are native to Virginia freshwater rivers, so I guess most of what I’ve pursued is an “exotic” from that perspective.
Well thanks! That makes me feel much more sophisticated and suave now that I know I pursue exotic fish. 
- Big D
Sure, why not?
Pretty much any fish introduced to an area outside its native range could be considered “exotic”. I was sort of thinking of fish that aren’t native to the US, ie from tropical south america, asia, etc., but actually it is interesting to talk about the fish many people target that, though native to the US, aren’t native to their particular region. In Texas that would be:
Smallmouth bass
Florida-strain largemouth bass
Redbreast sunfish
White bass
A fish that is not necessarily targeted, but caught nonetheless:
The Texas cichlid, aka the Rio Grande perch. Only native to the Rio Grande and Nueces drainages in the south part of the state, but have been introduced to freshwaters up and down the Gulf coast, as well as waters of the central Texas Edwards Plateau region.
Another anomaly in Texas - we have striped bass and redfish stocked as put-and-take fisheries in inland freshwater lakes.
exotics
Snakehead.
Freshwater Exotics
Piranha in FL canals.
Snakeheads in the Potomac river.
Palamino trout in PA streams.
Amber
I picked up an exotic dancer once at the Yellow Rose in Austin texas. Must have gone 115 to 120 lbs.
Forgot to add
Peacock Bass in canals along the FL Turnpike, as well as the Everglades.
DORK Fish
DORK fish 2 of em in one day