Spoofed in The Slayers episode Navigation! Invitation to Sairaag. Lina's gang is travelling on a raft by a river to an unfamiliar destination, they suffer from hunger and are relentlessly pursued by bandits and bounty hunters. Finally Lina has had enough and starts blasting around with her Dragon Slave spell, creating a new lake by the way.
Actually, the river in that one is the path between civilization and chaos, with the boat being order and the jungle being chaos. People either learn to swim in the rivers of madness or go mad or get killed messily.
Coppola has stated that the characters encounter increasingly primitive conditions the further upriver they go, to some extent becoming more primitive themselves.
John Carter's, Dejah's, and Sola's river journey leads them to an important revelation, but also gets them ambushed by Warhoons.
Another Klaus Kinski example, and one fitting the entire "obsession and insanity" theme of this trope, is the movie Fitzcarraldo. Kinski plays Peruvian rubber baron Carlos Fitzcarraldo, who dragged a steamship overland just so he could build a new rubber plantation on a previously unreachable river, regardless of the cost. Oh, and he was one of the founders of Manaus, Brazil.
See also Herzog's documentary Wings of Hope, about a girl who was the sole survivor of a plane crash in the Amazon and walked for ten days out of the jungle - and then 30 years later, Herzog brings her back to retrace her steps. Oh, and 'Little Dieter Needs to Fly/Rescue Dawn. Yeah, Herzog really likes this trope.
Dead Man: The eponymous title character is taken to the "river made of waters".
The Conquistador story arc of The Fountain (probably inspired by Aguirre)
The African Queen is an amusing example - the actual film has the characters not going mad, and instead falling in love and defeating the Germans (what, you expected a spoiler for that? It was during The Hays Code, there was literally no legal way to have a Downer Ending, given the premise), but according to Katharine Hepburn's book, the making of the film took its cast and crew through the sort of arc this trope normally describes.
In Rambo (the fourth movie), Christian missionaries hire/convince Rambo to take them up the river into Burma where they can help villagers with medical supplies, dental exams, and religion, but their journey is doomed from the start, beginning with Rambo killing a gunboat full of soldiers and ending with the village being raided and the missionaries being taken prisoner.
Gibbs: Let's put some distance between us and this island, and head out to open sea.
Sparrow: Yes to the first, yes to the second, but only insofar as we keep to the shallows as much as possible.
Gibbs: That seems a mite... contradictory, Cap'n.
In Without A Paddle, the characters get lost, lose their boat and supplies, and are attacked and pursued by a bear and violent locals.
In The Mosquito Coast, based on the novel of the same title by Paul Theroux, Harrison Ford is a Yankee inventor who takes his family to live in the jungle on the coast of Honduras. Their misfortunes culminate in a perilous river journey during which the inventor grows increasingly paranoid and finally winds up completely insane.
In Valhalla Rising the characters arrive in a mysterious land (The Americas apparently) via boat and subsequently fall to each and every one of these tropes ultimately leaving the now orphaned child standing on the edge of said river. Presumably wondering why he decided to get out of bed at all. This film is the purest incarnation of this trope.
Into The Wild is a partial example. The river is more of an obstacle than anything, and the kid is a Wide-Eyed Idealist who wants to go as far away from humanity as possible and is doomed from the outset. Instead of being trapped on a boat, he ends up trapped in a bus.
Constantly subverted in Lord of the Rings, as the characters explicitly go out of their way to avoid the rivers, roads, or even straight passages whenever possible, with the strong impression that something bad would happen to them if they followed the normally prescribed route.
Although they do actually journey for a considerable distance down the Great River.
During which they are tracked the whole way and shot at by arrows, Apocalypse-Now style. We also see Boromir get more and more unstable en route (in the book, it's because of Aragorn's uncertainty about where they are going). Legolas noted that they had to get off the river; at that point they were just trying to outrace the enemy. When Boromir's madnessbroke up the Fellowship, he inadvertently saved the mission. (Ironically, Gandalf had planned to break up all along and send the decoy hobbits to Minas Tirith.)
In the Swan's War trilogy the heroes travel down the river and to adventure the whole first book. They actually do much good in the standard epic fantasy way, but a river spirit influences one of them and he never really recovers and dies one year later by what is implied to be suicide.
The horror novel The Ruins by Scott Smith starts out with a group of twenty-somethings on vacation at the beach who decide to explore some old ruins inland. In The Movie, all but one of them die thanks to a sadistic, man-eating vine. In the book, they all die.
There is a book called Who Is the River that is about two guys going up a river in South America. The point of the trip was to find a set of ruins and make their careers. It didn't work.
In the Seventh Sword trilogy, there is only one river and this river connects all the cities of the world. Because the river symbolizes the power of the goddess that controls the planet, the river can flow in either direction and ships that travel on her waters may drop anchor in one location at night and mysteriously re-appear elsewhere by morning. Not only that, but the river is inhabited by flesh-eating fish that appear within seconds of someone entering the water.
In the Shirl Henke novel The River Nymph, the male protagonist grows darker and darker in character as the titular riverboat goes ever farther up the Missouri River and into the wilderness of the American frontier.
The journey of the City in The Inverted World. For over two hundred years, the massive mobile City has been pulling itself in pursuit of the optimum. It is a truly Sisyphean effort: even if the City reaches optimum, they cannot rest, because optimum is always moving. The City is doomed to struggle to move 1/10 a mile a day, every day, forever; an unending pursuit of the unattainable.
And in the novel version, geography eventually renders the goal literally unattainable.
The second expedition in the novel Water Music by T.C. Boyle about real-life Scottish adventurer Mungo Park and his search for the Niger. He found the river on his first expedition, but he came back for another expedition to find out where it ends.
In The Red Tent, Jacob crosses a fast river ahead of his family and servants, and has his famed vision of angels ascending and descending a ladder or staircase, as well as an alleged fight with one (which results in his thigh being dislocated.) He is shown to have a fever, and the other characters take his visions as delirium. This is an important point, as it is essentially where Jacob (fearful from his unexpected Vision Quest, and later jealous of his wealthy twin brother Esau) starts to listen to Simon and Levi's influence and become corrupt and greedy.
The Priest's Tale from Hyperion is a lot like this: the journals of a man hiking out into the most deserted wilderness of an alien planet, only for things to get progressively more insane.
The Mosquito Coast by Paul Theroux is about a Yankee inventor who relocates to the coast of Honduras, taking his wife and children along. Their experience in the jungle is a series of misfortunes and disasters, culminating in a perilous river journey during which the inventor grows increasingly paranoid and finally goes completely insane.
In Algernon Blackwood's "The Willows", two men on a canoe trip down the Danube find themselves in the middle of a willow-infested swamp with a thin wall between them and Another Dimension.
I Shouldn't Be Alive had "Escape from the Amazon". Only two of the explorers were found.
In The Gamers Alliance, Alent's infamous Threshold district is an urban version of this trope. Most people who enter it go gradually insane the longer they spend in there (and the deeper they walk into it), eventually ending up mad or dead. The very air, ground, buildings and narrow, labyrinthine and twisting alleys seem to be alive and hostile to any non-native, and the shadows play with trespassers' minds with sometimes fatal consequences. It later turns out that the people living in Threshold are in fact disguised demons whose chaotic powers have warped the district to suit their needs. The horrible visions which trespassers experience turn out to be manifestations of their own inner darkness and emotions which have been triggered by the demonic auras in the area.
Javan: The truth is that the only real darkness in this place is the darkness you bring in it yourself. Every sin, every repressed memory, every stray fear and blind rage. Everything people want to ignore about themselves. What's in here was always there, it's just a bit more... insistent in its existence in Threshold.
"That's how I learned what it means to be an American. To embrace the pioneer spirit, shoot everything that moves, drown my family in a river, and die of starvation somewhere in the midwest."
Its tropical twin The Amazon Trail also counts. And yes, you travel up the Amazon river. In a canoe.
Along the way, the encounter with Lope de Aguirre (see below) plays kind of like a brief, kid-friendly version of Apocalypse Now.
Let's Go Find El Dorado, paying homage to The Oregon Trail, combines the crossing of rivers and the catching of dysentery. If your wagon so much as touches water for more than a fraction of a second, your party members will get sick.
Part two of Jeff Vogel's Exile series has a section where your party must cross over a series of underground waterfalls, each one taking away some of your food. Eventually, a really big waterfall will make you lose all your remaining food, forcing you to scavenge (usually fighting off monsters along the way) or face starvation. It's also worth mentioning that there are no shops or training available along the way, and no way to identify the items you find (and you probably won't have enough space to take everything you find). Oh, and the caverns you pass are full of dangerous monsters...
Fallout: New Vegas's Honest Heartsexpansion pack involves traveling to Zion National Park with a caravan company. Your party gets slaughtered by tribals immediately after entering the canyon.
Sir Ernest Shackleton's Real Life expedition to the Antarctic. However, everyone survived and Shackleton was forced to travel the last leg by himself, over sheer cliffs because they crash landed on the wrong side of the island of SouthGeorgia, the only source of possible help for 5,000 miles in any direction.
When Robert Scott and Roald Amundsen raced to be the first expedition to reach the south pole, Scott's expedition found the Norwegian flag waiting for them. Then Scott's entire team died from scurvy on the way back.
Several Real Life expeditions into Darkest Africa inspired this trope, most notably Emin Bey's expedition to Equatoria, a vast and inaccessible swamp on the headwaters of the Nile. (A German-Jewish geographer who had been appointed Bey of the Turkish Empire, he claimed the region for either England, Egypt, or Germany, it's not clear which.)
After "discovering" Dr. Livingstone (who was doing just fine without him), the "journalist" Henry M. Stanley made a name for himself penetrating the headwaters of the Congo in the service of King Leopold of Belgium, executing uncooperative natives along the way, and claiming the Congo basin for Leopold's personal rubber fiefdom. His expedition is what inspired Conrad to write his book, after it came out what Leopold's men were actually doing in Stanleyville.
There were many, many doomed voyages into the interior of Australia, filled with some of the harshest desert known to man and landscape utterly foreign to Europeans. One notable mention was Charles Sturt, who nearly died multiple times and even took a boat with him to settle the debate about if Australia had an inland sea. Many Australian explorers barely came back alive and others died miserable lonely deaths. Surviving comfortably in the outback is perfectly possible, but they were too proud to ask survival tips from the natives (didn't help that Europeans and native Australians were prone to not understanding each other even when they had words in common- their worldviews were impossibly mismatched on many points). Ironically, there was an inland sea... once. Stuart and his fellows were just about 100 million years too late.
The first white explorers to take a boat down the Grand Canyon: Half of them died.
Deliverance was based on the author's real-life experiences rafting in Appalachia. Massively inverted in that the locals were incredibly helpful, and were excited to hear he was writing a book about the area!
Apropos of a related trope, the Donner Party is worth mentioning. Basically, a group of pioneers set out for California, ended up snowbound in the Sierra Nevada, and resorted to cannibalism, eating the corpses of those who died.
The first Western voyage up the Mekong River in Southeast Asia was pretty difficult, partly because the river isn't actually navigable up most of its length, and partly because most of the crew repeatedly caught tropical diseases.
The ill-fated Narvaez expedition of would-be Spanish conquistadors in the 1520s. Despite suffering from serious food and supply shortages and a near shipwreck prior to even leaving their base on the island of Cuba, and drifting over a thousand miles away from their intended destination, the expedition's leaders decided to go a-conquering anyway - with predictable results. Amazingly, after being stranded in the wilderness of what is now western Florida, enduring another series of shipwrecks on a few homemade rafts and being captured by a dozen or so successive groups of Native Americans, 4 of the expedition's original 300 members managed to wash up on the Texas shore and walk over 1700 miles to Spanish-occupied Mexico. Almost too surreal to be believed, but check out the whole story on That Other Wiki
The real life Lope de Aguirre who mutinied against his leaders during an expedition to find Eldorado (in itself a goal that fulfills this trope), and then led the soldiers and Native American slaves left alive on a hundred day march through the jungle to capture the main Spanish settlements in Venezuela, Panama, and Peru. At first relatively successful, the Spanish army offered free pardons to any of Aguirre's soldiers who would desert, at which they all did, leaving him to die.
Yermak Timofeevich, the Russian Cossack ataman and the first Russian to conquer Siberia, found it somewhat less than welcoming. He died escaping a clash with the natives, falling off a boat (into a river, yeah) and drowning due to his heavy plate armor. However, Yermak's quest was followed on by other Cossack atamans, and in the middle of the 17th century Russians reached the Pacific coast.
Quite in the lines of Lope de Aguirre in terms of tough luck (not so much in insanity) is Juan Díaz de Solís. He discovered the "Fresh Sea": Río de la Plata, an estuary so big it looks like a sea. They thought that it may be a good idea to go upriver, set their feet on the land and see if that pesky Eldorado was there. He didn't found it, what he did found was hostile natives, who killed him and his escort in full view of all the men aboard. Taking good notice, his second-in-command decided that it was about time to go back to Spain.
Captain Sir John Franklin's Arctic expedition in 1845. All Arctic voyages are hazardous, but Franklin's crew had an additional problem; several of the men developed lead poisoning, which impaired their judgement and made them more susceptible to disease.
Another arctic example: Andree's attempt to fly a balloon to the North Pole in 1897. Not only did they underestimate the difficulties of flying a balloon across a sub-zero wasteland, but they had virtually no knowledge of how to survive in the Arctic after crashing and having to walk back to dry land - on ice that floated northwards. Somehow they managed to survive for three months, despite almost walking in place, before they succumbed just as they reached a remote island; they weren't found until 33 years later.