Every time Usagi Miyamoto takes "one of Gen's short cuts" he winds up stumbling into a dastardly plot.
"Little Red Riding Hood" is probably the Ur Example. She was told to stay on the path, but she just had to go and take a shortcut through the woods... and the rest is vaguely-Freudian history.
In an animated adaptation of this tale, Hoodwinked! does this to the Wolf and Twitchy. After Red manages to escape from them, they contemplate their moves and decide they need to get to Granny's before Red gets there. Just by chance, Boingo appears, and tells them that he knows of a shortcut that involves going "over the woods and through the river", then realizes how stupid this is, saying "No....you don't want to go through the river, you'll get all wet." The scene cuts to the Wolf and Twitchy treading their way through a flooded cave that happens to be populated with bats. The Wolf comments, "Never trust a bunny with directions, Twitchy." He's also practically hitting himself for deciding to trust Boingo with directions. Case in point: Boingo scribbled down the (practically useless) map and directions on an Easter Egg.
Likewise, Red Puckett is put onto a longer land route to get to Granny's not because of a decision to take a shortcut, but because she was pushed out of a cable car cabin and fell several hundred feet.
Film - Animated
In Ice Age, the group takes a dangerous shortcut that isn't a shortcut at all, just so that Diego can hide the others from his clan.
Finding Nemo: On their way to Sydney, Marlin and Dory have to cross a trench. Dory has been told to swim through it, not over it, but Marlin insists that going over it is safer. They go over it, and end up surrounded by jellyfish.
Film - Live Action
It's a Mad, Mad, Mad, Mad World was one Long Delay after another. For example, Phil Silvers' character takes a shortcut on a dirt road at the advice of a local kid, only to find that the road goes through a river. He attempts to drive through anyway and loses his car.
Pretty much the whole point of Rat Race, in which six different people (often with family/sidekicks) try to be the first to get to a town in the next state. Hilarity Ensues as increasingly improbable circumstances slow them down - the helicopter pilot discovers her boyfriend cheating on her and runs out of fuel in the ensuing vengeful maneuvers, a "helpful" woman provides shortcut directions to one driver that sends them over the edge of a cliff because they didn't buy a squirrel, and so on. The movie was kinda remake of Mad, Mad, Mad, Mad World anyway, so that's to be expected...
Brian: Where the hell is the suit store? We've been walking for forty-five minutes!
Champ: Brick, I thought you said this was a short cut.
Ron: Well, is it a short cut, or not?
David Vincent saw The Invaders after getting lost "looking for a short cut that he never found".
A children's storybook based upon The Berenstain Bears features a Bear Scout troop hiking up a mountain. While the group take the longer way according to their map, Father Bear takes a shortcut — admittedly, it's a shorter route, but it is beset with nigh-deadly hazards.
The Lord of the Rings is the Trope Namer (it's a Hobbit proverb quoted by Pippin). In The Fellowship of the Ring the hobbits attempted to shorten their walk by cutting across country and ended up miles off course.
Their short cut was longer than it needed to be in order to avoid going past a nearby village inn. Pippin is heard reminiscing about the quality of their beer, and Frodo is immediately convinced: "That settles it. Short cuts make for long delays, but inns make longer ones."
This is later averted by Strider, who comments that "my cuts, short or long, don't go wrong." His shortcuts are faster...but they're not necessarily pleasant. Midgewater Marshes, anyone?
Later Zig-Zagged when he successfully takes the grandmother of all shortcuts through the Paths of the Dead. It's not actually any faster than the mundane route taken by the Rohirrim, but he comes out the other end with an invincible army of ghosts, so they forgive him.
In the second Warrior Cats story arc, a lone cat named Purdy offers to show the traveling Clan cats a way though the city rather than having the cats waste time traveling around it. He claims the whole time that he knows where he's going, but the Clan cats know it's not the quickest route (at one point they realize they've been traveling in the wrong direction all day; they're supposed to be heading toward the sunset). It also results in Feathertail nearly getting captured by a Twoleg and Tawnypelt being bitten badly by a rat.
Not so much a " long delay" as "getting involved in a secret Alien Invasion and given powers by a dying alien," the Animorphs begin their adventure by taking a shortcut through a construction site one night. In one book Jake makes a Deal with the Devil (or an alien who works for a devil-esque Sufficiently Advanced Alien) to avoid taking the shortcut and they still get involved in the invasion, only without their morphing powers and most them are killed but Earth is saved in the end. This is restored to the main timeline with a Reset Button where the "devil" rescends the offer before Jake can take it.
This trope also comes into play, albeit unintentionally, in The Unexpected, one of the latter ghostwritten books. Stowing aboard an airplane bound for Sydney to escape the Yeerks, hijinks ensue and Cassie finds herself in the outback. The only problem is, Sydney's on the east coast of Australia, meaning that plane departing from California had no business being over the outback. Explanations of this anomaly offered after the fact are curious and unsatisfying.
Live Action TV
Appears and is lampshaded in The 10th Kingdom. There are two roads leading to Wendell's castle, and the pair of unlikely heroes are on foot: they must choose whether to take the long and pretty path or the short and scary path. "Virginia, don't you think there's a chance that it's going around something? But... but one path has trees, and the other... argh!" They take the scary path. The fact this detour turns out to be necessary in order for Virginia to obtain the poisoned comb so that she can deal out the suitably hoist by her own petard, Karmic Death for the Big Bad only makes this hew even closer to the trope. ("It's the journey that matters," and The Quest usually requires that something very important be found or learned while the heroes are caught up in a seemingly random delay or distraction.)
Metaphorical version: On Deadliest Catch the Time Bandit crew tried to de-ice their ship faster by blowing huge chunks off with a large firework. They did manage to get rid of a ton of ice — which landed on their coiling machine so now they have to resort to "Neanderthal fishing" and have a guy looping the rope by hand.
One episode of The Mighty Boosh has Vince suggesting a shortcut to Howard that leads them both into the middle of nowhere. When Vince explains himself as having tried to follow the long red road on the map, Howard rightly points out that it's actually a raspberry bootlace.
Inverted in the Doctor Who serial "Dragonfire"; when Ace boards the TARDIS at the end, she's miserable because she assumes the Doctor is going to take her straight home to Perivale on Earth, a place she loathes. The Doctor, however, has decided she'd make a good companion, and offers to take her home via the 'scenic route' — which he outright promises is going to be much longer and more dangerous, but infinitely more interesting.
A major aversion occurs in the Keeper campaign of Age of Wonders. If you can remember the way through the Underground Path, you can literally walk straight past an entire map of enemies. If you have the haste spell and click fast, you can complete the entire mission in under 30 seconds.
Racing games, especially ones that are not serious (Burnout, Mario Kart) often include shortcuts that, if not executed properly, will cost the player even more time than the shortcut is intended to bypass.
In Mario Kart's case, sometimes the longer "shortcut" will have an item box to compensate people who decide to use the path. The paths are usually less traveled by most racers, making them safer from being hit by most items.
In the Micro Machines series of racing games, some of the courses are wide open and shortcut opportunities appear to be plentiful. Go too far off course or stay off the course for too long, however, and the game will immediately abort your run and place you all the way back at the point where you first left the track.
In Baldur's Gate II you're asked to destroy a beholder cult called the Unseeing Eye, and are informed that it's far too powerful and you have to retrieve an artifact to destroy it. This involves going to an underground city to get half of it, then through a town of undead, then through a lair of beholders, before you finally get the other half. Alternatively, you can just start killing its cultists and kill it when it shows up to stop, because the point about the Unseeing Eye is that it's a blind beholder. Which makes it less formidable than the normal beholders you had to kill to get the artifact.
In Neo Quest II, one NPC in Act II remarks: "You know the saying: the shortest distance between two points is a straight line? Well, the longest distance between two points is a shortcut." Luckily for you, the player characters are not required to take such shortcuts.
In Nip and Tuck, Gus takes a shortcut to win a race he's losing—and ends up right in the middle of a demolition derby which reduces his truck to so much scrap metal. A long delay indeed!
"Let me say this again, you want to take a shortcut through the Desert of Certain Doom? You know the part of the map here with all the radiation and biohazard symbols on it?"
A recurring plot element and running joke in the Rupert Bear cartoon series is that all of Bill's "short cuts" invariably lead to some sort of strange adventure, but never where they wanted to go in the first place. In one episode, the two decided to split up and make a race out of it. Naturally, this time it's Rupert taking the proper route who finds himself in a land of adventure, which implies that it's not the shortcuts that lead to adventure, it's Rupert.
Has occurred several times in The Simpsons (most often at Homer's instigation).
Futurama "Are you sure about this shortcut?" "Not as sure as I was an hour ago."
In an episode of 2 Stupid Dogs, the big man's blind and buys the dogs to use them as guide dogs. The little dog's shortcuts eventually lead him to the top of a building under construction.
Stoked!: In ""Reef, Broseph and Emma's Totally Stupid Adventure", Broseph, Reef and Emma go into town for beaver tails (a local pastry), but stay too long and realize they're late for work. They try to take a shortcut through the woods, but end up lost in the woods for the day. Hilarity Ensues.
Wacky Races: Dick Dastardly once took a short cut that was blatantly shorter than the road he should have taken and ended up falling victim of a booby trap at a place he trespassed and the Mean Machine had to be practically rebuilt part by part. By the time Muttley finished rebuilding it, the land owner learned Dastardly tricked him to stop the other shortcut users and started shooting him. By the time he reached the finish line, he was in last, as usual, the Mean Machine had holes all over its body and it fell apart as Dastardly was about to cross the finish line.
Invoked in an episode of Adventures of the Gummi Bears, where Cavin is transformed into an ogre in order to infiltrate the ranks of Duke Igthorn's army. After accidentally "capturing" Cubbi, he ends up taking point on the Duke's next invasion, which he tries to sabotage by leading Igthorn and his ogres on a variety of wild goose chases in the guise of "shortcuts."
One episode of Beavis and Butt-Head has the two miss the bus back home; rather than walk home, Butthead suggests they take a shortcut. The duo end up in a different neighborhood and end up spending an entire day just to get back to their school.
In The Smurfs episode "The Trojan Smurf", the Smurfs must carry a big statue of Papa Smurf (which is really a Trojan Horse for Gargamel to infiltrate the Smurf Village) to the village, but cannot get it across the river because the bridge is too small. Brainy suggests a "short cut", which ends up taking the statue down a very steep slope, only to fall into a raging river that ends in a waterfall that Bigmouth is taking a bath at the bottom of, and said ogre mistakes the statue for a talking Papa Smurf doll.
Gen's bad shortcuts are given a lampshading in the Teenage Mutant Ninja Turtles (2003) episode "The Real World part 1", when Leonardo, Usagi, Gen, and Lord Noriyuki find themselves at a cliff, and then are soon attacked by Neko Ninja.
Leo: This is the way to Edo?
Gen: It's a shortcut.
Usagi: Your shortcuts will be the end of us.
In the Rocko's Modern Life episode "Road Rash" Heffer tells Rocko to take a shortcut on their motorcycle trip. They end up passing numerous landmarks including the Egyptian Pyramids, Stonehenge, a Venetian canal, Moai Statues on Easter Island, the Eiffel Tower, Rocko's house, and the Taj Mahal. Heffer says that must have saved them hours. While they were previously 500 miles from their destination, now they are only 499 miles away. Rocko asks him if he is reading the map right.
The Donner Party, whose decision to take an obscure and untested shortcut (instead of the longer, but more established route) west to California turned a journey that typically took four months into a desperate ordeal that lasted over a year. The winding 'shortcut' led to the Donner Party getting trapped in the Sierra Nevada mountains during the harsh winter months with grossly inadequate supplies. Faced with starvation, they were eventually forced to resort to cannibalism to survive. It wasn't just taking the shortcut. They were supposed to go with a larger group, but they were late, so to catch up, they took a shortcut through the shortcut.
One of the more hilarious consequences of GPS navigation for cars. Most drivers will tend to stick to the routes they are familiar with, but when they get a GPS some will decide to take its routing instructions because it's supposedly shorter or faster. Murphy's Law will inevitably kick in and they'll find the shorter route will have construction, recent changes to streets (such as switches to 1-way) that aren't reflected in the GPS database and other comedic impedements. Also the number of delays they will face will be directly proportional to how urgently they have to get to their destination. If your GPS has choice systems, you might have cases where there is one route that is shorter in terms of miles traveled, but the travel time is longer (for instance, in the mountains, going on seasonal roads over mountain passes), while the other route, although longer in miles, turns out to be faster in time (because it uses Interstates and roads that are year-round).