Subtrope of More than Meets the Eye. A character is not as tough as their physical appearance and/or personality suggests. Basically the opposite of Hidden Badass (though they can go the cowardly lion route).
Paper tiger is a literal English translation of a Chinese phrase, meaning something that seems as threatening as a tiger, but is really harmless. This Chinese colloquialism is similar to the English phrase "its bark is worse than its bite". Still...
The phrase is an ancient one in Chinese culture, but sources differ as to when it entered the English vocabulary. It is found translated to English as early as 1836, in a work by John Francis Davis.
Compare with Feet of Clay, which is when they purposely claim to be more Badass then they are, Contrast this to Badass on Paper, where the character isn't very impressive in person but actually performed all the impressive feats that are the basis for his or her reputation, Mugging the Monster for the complete opposite (finding that a weak looking individual is much more dangerous than they seem) and The Worf Effect, as it seems that this applies to the Worf him/herself in context, whereas The Worf Effect refers to the over-arching phenomenon of "stock 'tough' character handed ass by tougher one."
Bellamy the Hyena bullies other pirates on the island of Jaya and has spring-based powers with enough concussive force to destroy buildings. Protagonist Monkey D. Luffy and his first mate Roronoa Zoro let themselves get beat up by him under the idea that he has not wronged them. Once he does, however, Luffy challenges him, and Bellamy gets stopped cold with a single punch.
This may not be the best example though, as it's really more to showcase Luffy's strength. Bellamy isn't actually that weak, he just picked on a bigger fish.
Another example would be the fake Straw Hats, who talk a good game while nobody spotted the ruse, but who fall apart even faster than the (rather powerful) crews they'd hoodwinked when push comes to shove. It ends badly for them. Especially those left to the tender mercies ofCaribou.
In the English Funimation dub for Dragon Ball Z, Majin Buu calls Vegito exactly this during their fight. He is very much mistaken though.
Raijuta Isurugi from Rurouni Kenshin boasts all the time about his skills at kenjutsu, and how it should always be a murderous technique. In the end, he's revealed to be a phony Sore Loser who never actually killed someone.
The Military Police Brigade in Attack on Titan only accept the top ten recruits of each trainee class so their members are inherently the best and brightest the military has to offer. But their tendency to neglect their training and serious duties has left them the least capable branch and Jean noted when on a mission to save the captured Eren, its members are easily devoured. In comparison, the Survey Corps and the Garrison are more experienced and prepared to fight Titans.
The Wizard of Oz (1939). When the Cowardly Lion first appears he acts in an aggressive manner, charging the group and challenging them to a fight. When he tries to attack Toto, Dorothy smacks him on the nose and he starts crying. Granted, the Cowardly Lion also turns out to be a Crouching Moron, Hidden Badass later on.
In The Naked Gun, one of the members of the council of evil calls America "a paper tiger."
Eponymous Paper Tiger where the boastful British private tutor Ray Bradbury loses his cool and is ultimately, extremely humiliated but finally redeems himself in the eyes of his student Koichi Kagoyama when, faced with immense danger that would cripple anyone with fear, his innate courage begins to shine to his own disbelief.
In Mr. Smith Goes to Washington, the press corps call Jefferson Smith a "paper tiger" to his face, telling him that he was only appointed to fill a seat in the Senate and vote the way Senator Payne wants him to, which chafes the idealistic young senator.
Osten Taylor from Survivor: Pearl Islands was a buff bodybuilder who had absolutely no idea how to rough it out in nature, almost drowned in a challenge, became convinced that a pelican was out to get him, and ended up being the first contestant to quit Survivor.
Crystal Cox in Gabon, the six-foot-three Olympic gold medalist who had one of the single worst athletic performances in the series, culminating in her missing a slam dunk on a basketball hoop that's shorter than she is.
NBC’s One World: ex-delinquent Jane ended up feeling this way. Normally strong, tough, streetwise, with a smart mouth, a camping trip with their guardian and the other girls brought out a side of her she never really expected: being terrified of puny little creatures and insects of the woods.
Parodied in Calvin and Hobbes. Calvin comes across the term in a book he's reading for homework and asks his tiger Hobbes what the definition is. Hobbes responds that it's a tiger with a newspaper route, much like a paperboy. One Beat Panel later:
Paranoia supplement Acute Paranoia, adventure "The Harder They Clone". The doorman at a nightclub looks like a character in The Road Warrior: huge, black leather tunic, rippling muscles, and scars. It turns out the PCs can easily kill him since he's unarmed and unarmored.
From Tales of Monkey Island, Bugeye is a bald, tattooed pirate who disrespects the main character and generally talks tough. But once you need to get information out of him, you find that the slightest bit of pressure will make him squeal.
Sir Prancelot of Scufflewick from Drakensang: he wears a full plate armor, has a cool winged helmet and wields a large two-handed sword. He's also a complete wimp who won't admit his failures and runs away from goblins.
In Ace Combat 3: Electrosphere, UPEO itself is regarded as one of these, especially highlighted in the mission "Paper Tiger". To further push the point, their planes are obsolete hand-me-downs from both General Resource and Neucom, which are the only things making them anywhere near a relevant military force that can keep the two corporations in check.
The Nali of Unreal are 7 feet tall, have four arms, and are quite muscular. They are also completely incapable of fighting and get easily destroyed by anything that attacks them.
The Batarian Hegemony in Mass Effect is said to be this. They're a rogue state that's essentially Space North Korea, and the only way they can effectively war with anyone is hiring terrorists and pirates to launch proxy attacks on human colonies, which caused the Skyllian Blitz and the Battle of Torfan. Though in the past they annexed an independent asari colony and shelled a salarian planet, by the time Mass Effect 3 rolls around they're the first race to be curb-stomped by the Reapers, though considering it's the Reapers it goes without saying.
It's pretty clear Teyrn Loghain Mac Tir in Dragon Age: Origins is not the political powerhouse he might portray himself as. Highever is openly rioting against him, Redcliffe and nearly the entire Bannorn is warring against him, and according to Bodahn, the Darkspawn burn down Gwaren, his own fief, leaving him with Denerim under his military occupation and Amaranthine, which Dragon Age: Origins – Awakening reveals was increasingly divided because of what Arl Howe did. Actually losing to him at the Landsmeet pretty much requires the Warden to actively avoid the political sidequests, or for them to go out of their way to be a jerk to people they're trying to win over.
Part of this can be attributed to the prejudice Loghain faces from being a former commoner. While his Rags to Riches story has made him popular with the people, his fellow nobles actively despise both him and his daughter. It doesn't help that his main political ally is Howe, a despicable noble simply in it for a power grab, who's openly disliked by everyone. The fact that they plot the destruction of the Cousland household at the start killed any chance of them being able to sway others to their side.
In Avatar: The Last Airbender, Hakoda tries to pick a fight with a tough-looking prison inmate by shoving him, but instead of fighting back the inmate says "that hurt my feelings!" Averted a few minutes later when someone starts a prison riot, causing that same inmate to scream, "Forget controlling my anger!" and rushes out to fight with everybody else.
Johnny Bravo. He's a pretty muscular-looking guy but he's always getting beaten up by the women he flirts with. Which is especially weird considering in the very first episode he was able to successfully wrestle A CROCODILE!
Tiger in Skunk Fu!. Formerly a powerful warrior, after losing to Dragon, he's become a cowering wimp.
Cerberus from My Little Pony: Friendship Is Magic (Yes, that Cerberus). True he's a fierce three-headed monster quite literally from Tartarus that's the size of the average house, but all it takes to tame him is a belly rub and a friendly game of fetch.
Season 4 might have subverted this. Though friendly enough to the ones he's not guarding, he was the one thing keeping Lord Tirek, the worst and most dangerous villain to appear yet, from escaping Tartarus.