The Chesapeake and Delaware Canal. Public domain work of Army Corps of Engineers.
Very early in Americas history, before railroads and airplanes and highways successively made America more reachable, there were only two alternatives for transit: the covered wagon/horse and the ship. Even in the 1600's, shipping was surprisingly well-developed at sea, and a trip across the Atlantic often took far less time then a similarly distanced trip across land, while the ship itself could carry far more cargo far more affordably then a similar number of covered wagons. The result was that coastal areas with ports became highly developed centers of wealth, while Appalachia and those areas away from ports became the distinctive "redneck" culture of charming economic ne'er-do-wells we all know and love.
In between theses two extremes were the lands along improvable seaways, and these would prove critical to the further development of America away from the East Coast. The most famous of these is the Erie Canal, built in 1825, from Albany to Buffalo through New York State. Combined with the Chicago Ship and Sanitary Canal, built 10 years later, linking the Chicago River to Lake Michigan, you had for the first time a true continuous seaway from New York City to the Mississippi River and the vast new lands beyond. The immediate result was a massive outflow of westward settlers, filling out the areas we now popularly know as the Midwest, and creating a market for mail-order goods that would be essential for the further development of the West. In addition, the vast cattle and grain lands of the West supplied the Chicago Stockyards, Chicagos first great manufacturing industry. Lastly and still importantly, the economy of all the great centers of upstate New York was built by cargo passing through the Erie canal.
In more recent years, the Chicago Canal and the Erie canal have both become largely irrelevant due to the increasing draft of freighters, but before they did, the intense increase in interest and investment in Great Lakes Shipping built the iron boat fleets. The iron boats now criss cross all 5 Great Lakes and the rivers that feed in to them carrying Iron Ore from Ontario, Minnesota, and the Upper Peninsula of Michigan to steel mills in Pennsylvania (through Erie, PA) and Indiana (through the Port of Gary). Stepping in to their place, the brand new Saint Lawrence seaway, easily deep enough for all but the biggest ocean-going freighters, has replaced the Erie Canal running from Lake Ontario to the Gulf of Saint Lawrence along the Saint Lawrence River, and a new steel mill has opened up in Montreal to harness the iron fleets, while grain boats now dock at Duluth, Minnesota and Lake Winnebago (connected through the Winnebago river) to use the Saint Lawrence Seaway to reach Europe. Unfortunately, the Chicago canal has not been replaced, and the Chicago river is too shallow for a canal improvement to be sensible, so it is primarily used by local barges, often carrying iron ore from Tennessee and Alabama to Gary.
In the Ozark Mountains of Missouri, land still largely undeveloped except for the least of uses, even less then agriculture, the Osage river was once targeted for improvement. Many attempts were made to allow ships from the Missouri to access the resource-rich and mountainous regions of the center of the state. The constant turns and rapids of the Osage made it difficult, and finally, the building of a dam at what is now the Lake of the Ozarks without locks ruined the dream of Ozarkian navigation forever. A few wealthy people and vacation homes exist on the Lake of the Ozarks, and very little significant economic activity.
A similar but somehow more lucrative Upper Missouri received major improvements throughout the 1800's and 1900's. Originally ending at Kansas City, where it meets up with the Kansas River, the navigable stretch of the Missouri was extended first to Omaha, and finally to Sioux Falls, Iowa. The region is now a hive of industry and transportation, and used to be even more so. Even with competition from the railroads, the barges were still more useful for many needs, and remain so to this day.
Yet another story of gradually expanding navigation is the Columbia. The navigation head on the Columbia was Portland, Oregon, and indeed for this it was named, from the late 1700's until the late 1870's, where thereafter an intense rapid prevented most further transportation. It was only one unnavigable site, however, and otherwise the river remained well navigable to what is now the Tri-Cities of Washington where the Columbia meets the Snake, and so even in the relatively undeveloped West it made sense to add a couple locks bypassing it. Shortly thereafter, a railroad, one of the oldest in the state, was built from Wallula to Walla Walla, Washingtons' oldest settlement, carrying fresh farm goods and resoures to port to be loaded on to ships and taken downstream, and in some cases even continue north to Alaska where they were needed absolutely and supported the gold rush. Ice also was transported, due to the divergent weather patterns of Eastern Washington (which freezes readily) and Western Washington (which stays fairly warm all year) on opposite sides of the rapids. Finally, in the 1930's, a couple hydroelectric dams were built on the Snake River, and it was realized that with one additional dam navigation could continue to Lewiston, ID; Lewiston, Idaho today is a center of the paper industry due to its location as a transportation center, in the desert halfway between two great timberlands.
Just because a river was unnavigable, however, did not mean it could not be useful for transit. Wagons too benefited form the relatively flat land and easy trails and abundant fresh water and game that even a tiny river provided. Five different wagon trails, to points in Oregon, California, Montana and Utah, all continued along the Platt River through Nebraska, a river known for being too shallow and unsteady even for canoe traffic. Likewise, sometimes navigability is in the eyes of the beholder - many of the rivers Lewis and Clark used are, even today, considered largely unnavigable, while many rivers in Texas, a state usually regarded as being all but without navigable rivers, such as the Trinity were once frequented by steamboats. Starting in the 1830's, short navigable sections of the Chattahoochee, mostly unnavigable that far north, near Atlanta were used for wagon ferries - the ferries have long since been replaced with roads that still bear their names, and they are still many of the most major roads in the city.
Fast flowing rivers, of the sort that are seldom navigable, are also often power sources for industry, and any river navigable or not can be used as a source of water and silt. Silt makes good farmland, and carries downstream minerals like the Gold that was famously panned along the various rivers of Alaska, and also the Diamonds found on the banks of the Ganges that introduced Europe to the Diamond in the 1700's. As a meeting place of navigable deep and broad and unnavigable fast moving rivers, fall line cities such as Hartford, CT, Augusta, GA, Pittsburgh, PA, Trenton, NJ, Baltimore, MD, and the great Industrial center of the confederacy Richmond, VA, where rivers come off a major incline, have been a valuable location for industry. Sometimes though, you can eat your cake and have it too: modern hydroelectric dams provide the same electric power that the old watermill provided mechanically, and can have a concurrent lock for shipping, such as the various dams on the Snake River that bring shipping in to Idaho, often times even making an unnavigable reach navigable.
Georgia has gone the opposite of the Missouri and the Columbia - once home to three navigable rivers, two of them, the Oconee and the Savannah, have been largely cannibalized for irrigation and drinking water. Former ports such as Augusta are no longer reachable to even the most basic of traffic. A movement now exists to do similarly to Georgias last remaining navigable river, the Chatahoochee, which is navigable from Columbus, Georgia to the Gulf of Mexico, despite many dams and improvements made over the years to make river navigation possible, all in the interest of Atlantas (which is not served by the river) literal thirst and growth. In addition, environmentalists in California are trying to bust CA's hydroelectric dams - those don't support shipping, but they do support electric power.
There are also the stories of navigation never completed. A canal project from Washington DC to Ohio was going to create a westward route for shipping traffic from the Chesapeake bay, but was canceled largely because of the availability of the railroad and the Great Lakes system providing too little remaining demand. The Nicaragua Canal was a viable alternative to the Panama Canal that could have potentially served far more local traffic. The latter may still be built simply because the Panama Canal is beyond capacity, the former however will largely not be built because the Potomac River, like the Chicago, is too shallow for modern oceangoing craft.
In general, though, riverine navigation is no longer a priority for modern government infrastructure, and Georgia is frankly a sign of things to come, a world that has largely lost faith in progress and edges more and more to mediocrity and an assumption of good results nearly every day. Less and less are people interested in expanding outside of existing centers and ways, preferring instead to blindly favor what already exists. This combined with radical environmentalism seems to indicate that America, and most of the worlds, days of canal building and extending the great seas to where they are needed are over. It is no wonder that Americas middle class and business base does not grow, as America itself does not grow, favoring only what already exists to the obvious benefit of the current wealthy.
Current Marine Highways of the United States, 2010, public domain work of US-DOT