When the heroes cannot directly challenge the villain or his mooks they disguise themselves as monsters or build something that's basically a tank with a threatening exterior. Usually relies on intimidation more than any actual weapons. When villains resort to this tactic, it's a Scooby-Doo Hoax.
The Life and Times of Scrooge McDuck from Don Rosa - the first chapter when Scrooge scares the Whiskerville away by making a fake ghost. They were so scared that, years later, all the Whiskervilles have white hair (their first appearance showed them black and brown haired, so it wasn't a family trait before that).
A repeatedly used plot element in lesser Donald Duck comics - a variant involves making some idol worshiped by primitive people appear to speak and tell them to stop roasting the heroes or whatever.
One Sam & Max story ("Monkeys Violating the Heavenly Temple") has Max about to be used as a sacrifice for a volcano cult. Sam tries this trope, covering himself in mud to ape the volcano god the cult worships. Not only are the cultists not fooled, they beat the stuffing out of Sam.
Fables uses a psychological Anti-Hero version when a reporter discovers the Fables' (fairytale characters who are actually real) society, though with the belief that they're vampires. Ultimately they kidnap him and trick him into believing they are indeed vampires who have tasted his blood and will control him into committing suicide along with publishing him as a child molester should he ever release his discovery. The reporter gets scared out of his mind and complies, but is ultimately killed a few days later by one of the more evil fables acting on his own.
In Star Wars, Obi-Wan first appears by scaring away some Sand People who were about to kill Luke. He does this by dressing up in his old Jedi robes and making some weird-sounding monster noises, causing them to flee in terror. According to the associated materials, the sound he's making is that of the Krayt Dragon.
Kehaar in Watership Down, albeit only halfway intentionally - great coincidental timing on his, Bigwig's, and the weather's part make it appear to the Efrafans that the bird was summoned out of lightning by Bigwig.
The original short story The Legend of Sleepy Hollow is a very early example of this one, especially if you subscribe to the interpretation that Ichabod Crane is a meddling jerk rather than a protagonist.
Galaxy of Fear has a book where a Jedi ghost repeatedly terrifies Tash to try and spook her away from a threat, because until near the book's end she is only vaguely aware of him and can't understand what he says. He can't actually do anything to her, but it seems like it for a while.
The Little Golden Book The Lively Little Rabbit has the rabbits and an owl build a long dragon costume out of tree bark and leaves, with all of the rabbits underneath it and the owl's wings protruding. It's a surprisingly awesome-looking dragon. It succeeds in scaring away the mean old fox.
When Bo and Luke were mistakenly declared to have drowned on The Dukes of Hazzard they faked a haunting by coating the General Lee with glow-in-the-dark paint and having Cooter rig it to run by remote control, using it to intimidate Boss Hogg to prevent him from blaming them for a theft. Subverted in that Boss Hogg isn't fooled for more than a few moments, and immediately suspects Cooter's involvement.
Serenity herself was used in such a fashion in a Firefly teaser.
Wash: Every man go back inside, or we will blow a new crater in this little moon.
Jayne(later): Damn yokels, can't even tell a transport ship ain't got no guns on it.
On McHale's Navy, the crew of the PT-73 fakes their deaths and comes back dressed as ghosts to scare Binghampton into tearing up the orders that were going to get them all transferred.
This is the modus operandi of The Phantom. The natives of his home country think he's an immortal personification of justice and protection, when he's actually the great-great-great (and so on) grandson of the original Phantom, with a Charles Atlas Superpower. Stories generally climax with him using a Scarecrow Solution to convince criminals that he's immortal.
The Avatar: The Last Airbender episode "The Painted Lady". After the Gaang accidentally makes things worse, they decide to use this solution to correct their mistake and scare a corrupt Fire Nation army out of the small village they were persecuting: Toph, Sokka and Appa create fog and an overall ominous and creepy atmosphere, while Katara dresses up as the Painted Lady herself, with help from Aang regarding her powers.
The Venture Bros. episode "Escape To The House of Mummies Part II". Dr. Venture, sitting on Brock's shoulders and dressed in a green blanket waves a flashlight at cultists to save Hank and Dean. It doesn't work:
"That's just a flashlight. Kill them!"
Operation Fortitude, used by the Allies to conceal their true intentions of where they were invading France in World War II, included the use of dummy inflatable "tanks" that deceived German intelligence into thinking the Allies had a couple of extra armored divisions in reserve.
The American Civil War included the ''Quaker Guns", dummy cannons that were really just painted logs, employed by both sides occasionally and used succesfully by the Confederacy a few times.