When Europeans and other non-indigenous settlers first arrived in North America, most cold-water habitat supported salmonids of some kind (trout, salmon, char, grayling). 

A Rio Grande Cutthroat Trout, caught by the webmaster on a recent trip to New Mexico.

East of the Great Plains, where Europeans settled first, these fish were Brook trout and Lake trout (both Char), and Atlantic salmon.  

The Great Plains themselves never supported trout, but as the elevation gain in the Rockies once again cooled the water enough for trout to thrive, a completely different set of native species appeared.  These were mostly different sub-species of Cutthroat trout (first described by Lewis and Clark, and designated species Clarki in the scientific - Latin - classifications). 

In isolated valleys of the desert Southwest, including parts of New Mexico, Arizona, Nevada, Utah, other species developed where elevations cooled water sufficiently.  These include Apache and Gila trout. Arctic grayling flourished in a small pocket of western Montana. In the hilly, intermountain gap between the Rockies proper and the high west coast ranges, Bull trout (another char) and "Redband" trout - close genetic cousins to the coastal rainbow, flourished.

On the west coast, the Rainbow trout dominated, both in its familiar stream resident form, and as "Steelhead", sea-run rainbows that return to fresh water to spawn.  Coastal cutthroats shared much of the same river habitat with bow and steelhead, and also made their own sea runs, though usually sticking close the coast.  California developed its own species in the High Sierras, the Golden Trout, as well as the Piaute cutthroat, and the beginnings of the Lohatian cutthroat range.  Not to mention the multiple species of Pacific Salmon.

Today, genetically intact populations of native fish are rare and getting more rare.  For a variety of reasons that seemed compelling at the time, many states stocked exotic species into their cold water fisheries during the 19th and 20th centuries: brown trout, rainbow trout (east of its native range), and brook trout (west of the plains).  This has had a devasting effect on the native species.  Cutthroat, for example, hybridize readily with rainbow trout ("cut-bows"), and get out-competed by brook trout in cold water headwater streams, and by brown trout in larger, warmer streams.

Today there are efforts to restore and expand native fish to some semblance of their original range though it's a huge challenge, complicated by climate change. 

For anyone seeking to fish for native fish in their native range, we offer these data.