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.
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 is a mild subversion in that he is the incredibly brave and talented gunman that he constantly claims to be, and a dutiful soldier who never backs down from a fight. Except it's all a lie; Slugslinger's confidence and ability are wholly reliant on his gun Caliburst, and when the ammo dries up, his 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 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).
Major Man from The Powerpuff Girls was a one-shot character who at first seemed like an exaggerated Expy of Superman and a hero who might even replace the girls. But as it later turned out, he was not only this Trope, he was an Attention Whore who was purposely arranging for crimes and disasters to happen so he could fly in to stop them; he couldn't handle a real one if his life depended on it, and it wasn't hard for the Girls to expose him as the fraud he was when the newest giant monster came into town. Who was a friend of theirs doing them a favor, apparently.