During one episode of Rurouni Kenshin, the Shinsengumi encounters one of these... who not only lays claim to enormous feats of blood-soaked bravery, but also the name of 'Battosai'. In other words, he's claiming to be Kenshin, the man who basically saved the country singlehandedly, but retired from his killing ways to be a man of peace. Kenshin doesn't particularly care, but his friends are incensed when they find that the fake has been pressing the local shopkeepers for money based on his proclaimed reputation. In the end, a professional killer shows up wanting a fight with the 'Battosai', however, and the fake is proven quite incapable of actually fighting... however, the Shinsengumi winds up forgiving him, when they find out that he's been using his drummed up reputation AND the money it's earned him, to run and protect an orphanage.
Of course, when the kids he was protecting were threatened not long after, he redeemed himself by completely ignoring a sword slash on his arm, grabbing a mook by his HEAD and throwing him at another mook...WOAH.
In an episode of Slayers, the characters meet a warrior who brags about killing all kinds of monsters, including the recently revived and defeated (by the heroes) Dark Lord Shabaranigdo. He's not a coward however, as when confronted with a dragon on a boat ride (He volunteered to defend the ship during passage) he tried to stop it bravely, he was just completely ineffectual.
In one episode of the Slayers Special OVA, Lina and Naga get hired by a woman to help out her son Jeffrey, who is a pathetic aspiring knight overconfident in his abilities. Jeffrey actually faints at the sight of blood, but luckily his mother comes along in disguise and beats up anyone who badmouths her son with a warhammer.
Ash's Oshawott from Pokémon. While this crops up occasionally in the anime, he makes it apparent, putting on a cocky attitude until he faces an opponent that is actually challenging, such as the Grass-type Pansage or his own evolved form.
He actually managed to beat Pansage after a bit of encouragement from Ash, however.
Scourge from Warrior Cats used to be one, claiming to have killed foxes and ripped teeth out of the mouth of dogs. Then he Took a Level in Badass and was actually able to do the stuff he claimed to be able to do.
Subverted with Nanael from Queen's Blade. Yeah, yeah, glorious, strong, smart, perfect. Then why are you so skittish around danger, hmmm? Play it cool. Oh look, here come the bad guys, and its time to live up to your talk. And these ain't mooks. You've got Melona who's basically the T-1000 except harder to kill, you've got an ancient spell-casting necromancer princess, and a scythe-wielding ghost girl with an army of evil spirits at her command. They give many of our main characters trouble one-on-one. You've gotten yourself into a mess this time, girl. And... she blows the ghost girl and her evil spirits up with a slice. Then hammers the revived ancient necromancer princess in the face. Then turns our resident T1000 into a goo tornado with a drill kick, sending the ghost girl and ancient princess right along with her. Pretty much effortlessly. Then she flexes her arm, places her other hand on her bicep, and declares "Nanael is so cool!" Yeah, it turns out that not only is Nanael not the Miles Gloriosus, she is easily the strongest character that we've seen fight to date. She had to be nerfed in season 2 just to give the protagonist a chance at winning the tourney.
Zonge in Toriko. The first hint that he's actually a cowardly weakling of a Gourmet Hunter is that every dish on his Full Course has a very low capture level. Fortunately for him and his two followers he is just lucky enough to avoid getting them killed when he inevitably gets in over his head.
Jean-Claude Magnum from Yu-Gi-Oh!. An action/adventure movie star, he would have everyone believe that he's the same as his characters. He isn't even close. In fact, Jonouchi (a legitimately badass street-fighter...before card games became the exclusive focus of the series) was originally a fan of his, but completely lost any respect for him after he was beaten by Mai in a duel, tried to kidnap her, and then acted like a Dirty Coward when Mai was in danger (and she never had anything but contempt for him to begin with).
In Yu-Gi-Oh! GX, there was Seven Stars member Abidos III, who was somewhat of a subversion. His great reputation as a powerful Shadow Duelist was fraudulant, but he honestly believed that he did, indeed, have the skills that he claimed to have. (He won all the time because people were losing on purpose to please him.) This was a subversion for another reason: When he figured this out during his duel with Judai, he did seem brave enough to fight for real, and was actually somewhat competant.
Subverted in Attack on Titan by Oluo. He is an obnoxious and loud-mouthed jerk towards Eren, constantly giving him a hard time, so it's easy to believe he's all talk. After Levi, he has the highest solo titan kills (39) in the elite squad.
Carta Issue of Mobile Suit Gundam: Iron-Blooded Orphans. She commands the Outer Earth Orbit Regulatory Joint Fleet and hams it up, using her position to order Gaelio around and behaving as though she's holding the thin red line between Earth and all the enemies of the solar system. Her position, while carrying some authority over the power blocs, is actually a ceremonial one and her forces have never been in a true battle. When she attempts parade-ground battle formations against Tekkaden, they wipe the floor with her.