DuckTales: Major Courage, a boastful actor who plays a Captain Space, Defender of Earth! on TV in "Where No Duck Has Gone Before". Not realizing that Gyro's rocket has taken him, Launchpad, and the boys into space for real, or that the aliens they've been captured by are also real, Courage walks around making hammy heroic declarations and challenging the aliens to fights as if he's on set. Then he attacks Buvolvan and gets smacked down. Realizing that the situation isn't just an act, he promptly escapes in the only ship, leaving the boys and Launchpad behind with the aliens.
Zapp Brannigan from Futurama is the patron saint of this trope. He will never rush in to a fight, but obtained a reputation of being a good fighter through his willingness to sacrifice wave after wave of his own men, while avoiding any risk to himself. If he does end up fighting, it's because he believes he has an overwhelming advantage, or is too stupid to realize that he's in danger.
Kim Possible: Adrena Lynn, the villain of the episode "All the News," is a TV-action star who claims to do "extreme" death-defying stunts, but in reality, she faked all of said stunts. Kim forces her to admit to being a coward who can't handle real danger by flying her around on a jet-pack.
Die Fledermaus from The Tick, who looks and talks the part of superhero but is the first to flee when danger is afoot. In fact, he doesn't just flee, he sometimes faints! Note that while "Fledermaus" is German for "bat", the literal translation is "flying/fleeing mouse", a perfect description for a total coward.
Slugslinger from The Transformers always claims to be a fearless and talented gunman, which seems to be backed up by his results on the battlefield, but in reality he is nothing without his gun Caliburst. When Caliburt's ammo dries up, Slugslinger's true cowardice is revealed.
In Transformers Animated, Sentinel Prime is one of these. While being Optimus Prime's equal, he considers himself superior, and is constantly bragging about how he should be fighting Decepticons while Optimus should be repairing Space Bridges. Then Starscream falls out of the sky, and Sentinel goes straight into Coward Mode.
Sentinel: What is that thing?
Optimus: Oh that's right, you've never seen one up close. It's called: a Decepticon.
And, unlike Optimus Prime, he's kept his fear of organics from when they abused both of them.
The cartoon Mickey's Rival introduces the character of Mortimer Mouse: romantic rival, shiny new car owner, taller than Mickey ever hopes to be...and an obnoxious braggart. Mortimer tries to impress Minnie by waving a red picnic blanket in a bull's face. Oh, how courageous he is, taunting a slobbering, snorting brute...while there's a fence in between them. The fence of course is actually open, and Mortimer only needs two seconds upon realizing this to not only haul ass out of there, but to throw the offending red blanket on top of the girl he was trying to impress. What a guy.
Zigzagged with Sir Tuxford in Adventures of the Gummi Bears. He's like this most of the time, but he can be somewhat brave if the situation warrants it; he's just slowing down in his old age.
Daffy Duck starts out as one of these in Draftee Daffy, right up until the moment when he gets a phone call informing him that "the little man from the draft board" is on the way to see him.
Still, it can considered mildly averted when noting Daffy's exploits in other wartime cartoons; he may be a coward, but he does have his moments.
Made only worse by his frequent bouts of ignoring his super powers. Despite being fairly invincible (as the plot demands) his "Hero Shield" power is just grabbing an innocent bystander and using them to soak up bullets for him.
Gaston in Beauty and the Beast could probably fit this. He is thought of very highly in the village for his various accomplishments (which are not really explained beyond hunting, being good-looking, spitting, eating 60 eggs, stomping around in boots, and decorating with antlers) and is brave enough to hunt down the Beast only when he has a mob in front of him. When he's held over a cliff, he starts crying and begging to be saved.
Gaston: Let me go! Please! I'll do anything! Anything!
The My Little Pony: Friendship Is Magic episode "Boast Busters" introduces the Great and PowerfulTrixie, a traveling magician-type unicorn (female; no Always Male or other Double Standards in this show), whose show involves boasting of her magical superiority and using cruel tricks to show up anyone who dares call her out. She also claims to have vanquished an Ursa Major, so when two young unicorns who buy into her stories are told not to believe it unless they see it, they go out and bring one to town, eager to see their new hero in action. Trixie, naturally, freaks out at the sight of a giantbear monster, and is forced to admit that she made up the story of having vanquished one so she would look good. Once the creature is defeated by Twilight Sparkle, however, she promptly falls back on her old arrogance: "You may have vanquished the Ursa, but you will never have the amazing, showstopping ability of the Great and Powerful Trixie!" (Appropriately, she exits with a really bad Smoke Out).
Played with in her return appearance, "Magic Duel," where Trixie's sub-par magical prowess is greatly boosted thanks to the powers of the Alicorn Amulet. The fact that the Amulet is simultaneously corrupting her mind means this doesn't go well. In the end, Twilight is the one who has to deceive Trixie into believing that she has unparalleled magical talent, in order to trick her into removing the Amulet.
Lucius from Jimmy Two-Shoes. In one episode when he believed that a moon beast might threaten Miseryville, he rode up into space to defeat it. The moment he came across resistance, he freaked out and was defeated.
A rare female example is Numbuh 86 from Codename: Kids Next Door, definitely. She yells at, insults, and intimidates any operatives who are subordinate to her like some Drill Sergeant Nasty... But then she quickly cowers and grovels when Numbuh 362 - her superior - gets angry at her. And in "Operation: E.N.D." when Chad tried to send the Moonbase hurtling into the sun, she did nothing but panic and lie on the floor sobbing (it was a pretty pathetic display, most fans would agree).
And in "Operation P.O.O.L", Negative Numbuh 4 qualifies just as much. To all the kids, especially his own minions, he is seen as a fearmonging tyrant bullying everyone into doing his bidding. However, his Fatal Flaw is that, like everyone from the Mirror Universe, he is the opposite of his own real world counterpart and thus a Dirty Coward in contrast to Numbuh 4's braverly and boldness. This was revealed when he started shivering in fear to Numbuh 4 challenging him to a dual and even orders his minions to fire in an act of cowardice. It's also possible that he might secretly love Rainbow Monkeys since the real Numbuh 4 hates them.
The Little Rascals episode "The Zero Hero" has two examples. When Darla is on her date with Captain Muscles, he stops the bank robbers, but one of them acts Genre Savvy and deflates his costume. After Captain Muscles runs away, Alfalfa comes along dressed as Alpha-Man, but faints after Darla tells him that the bank robbers are not his disguised friends.
Samurai Jack: Da Samurai shows up at a tavern and boasts of being a highly skilled samurai, bullying the other customers who are afraid of him, but he ends up Mugging the Monster by provoking Jack, who reluctantly agrees to fight him outside. Jack already knows that his opponent is nothing but hot air: he cuts two sticks of bamboo and tells Da Samurai to take one, saying he's not worthy to face Jack's sword. The result is a Curb-Stomp Battle in which Jack runs circles around his increasingly angry opponent, effortlessly thwarting all of his attacks while humiliating him with smarting blows; each time, Jack gives Da Samurai an aphorism about the self-defeating nature of arrogance, and eventually cracks through his suit of Fake Muscles to reveal him as a scrawny guy with a pot belly. Then an army of robot bounty hunters appears out of the woods. Da Samurai is incapacitated while trying to flee, and Jack saves them both by destroying every single one. In the immediate aftermath he apologizes to Jack, admitting he isn't hot stuff like he thought he was, and what Jack did was amazing. Just then he sees that the destroyed robots have reconstituted themselves into a giant monstrosity which is rearing up behind Jack, and pushes Jack away from its beam weapon while getting hit himself. After putting it down for good, Jack tells Da Samurai that he has taken the first step on the true path of the samurai, and the next moment he's calling Jack sensei and begging for more instruction.
Felix the Cat, during the Van Beuren Studios era, encounters Old King Cole, who brags about his supposed heroics but then runs an hides from anything he perceives as a threat. Eventually, the spirits of pasts kings get tired of his bragging and proceed to "knock the wind out of the old windbag", and Felix has to face his own fears to rescue him.
Boo Boom! The Long Way Home: Christopher is this. He really likes to see himself as the hero and most important member of the group, and constantly brags about his many skills, but his coward nature and being the Plucky Comic Relief makes it impossible for him to live up to these claims.
Woofer, the bloodhound from Clue Club, can be this. He and Wimper (his basset sidekick) are usually obedient to Larry, Pepper and D.D., but Woofer tends to brag about how he solved the crime when for the most part he hadn't done squat.