And, unlike most characters with Small Name, Big Ego syndrome, he's more or less aware that he doesn't even begin to meet the protagonists' level of strength. He just puts on a good act. When he sees for himself just how freakishly strong his opponent is, he starts panicking on the inside.
The Z fighters do acknowledge a few times that they think it's better Hercule take credit because they don't want the fame and also don't want people to realize just how crazy powerful some of these fights are getting because it'd freak them out.
Although he actually is among the fighting elite from the moment he's introduced, and by the end of the series legitimately ranks among the strongest fighters in the universe, Vegeta has a tough time seeing himself as anything but the best, period. By the end of the series, he has finally managed to accept that Goku is the better fighter, but it took multiple Break the Haughty moments, as well as him being killed twice, for him to do so.
Boss from Mazinger Z and Great Mazinger thinks he is the smartest and biggest Badass ever, the best biker around and a real ladies man, and people would pay for the chance to attend his birthday party (not joke. In episode 20 He tried to have his classmates paying for tickets. And he was shocked when all girls ran away from him screaming). Everyone else knows he is the Butt Monkey. Hence, when The Hero Kouji showed up, showing he was a real Badass, and a better biker and getting all girls -especially Sayaka- crazy over him right away, Boss understandably was not happy, and he constantly tried to showing Kouji up with very little success. He went so far to build his own -goofy-looking- Humongous Mecha using metal scraps and junk from a rubbish dump, and claimed it would replace Mazinger-Z itself. Tip: It did not.
Black☆Star from Soul Eater. He is good at unarmed combat, but he'd have to be a deity before that ego would be even remotely equivalent to his personal power level. He specifically claims to be more powerful than God.
There's also the Equippable Ally Excalibur, who really is as powerful as he says he is. The problem is that his ego transcends his power level- he's so insufferable and downright annoying that no-one can stand to be around him. Tellingly, when he shows up later on in the manga, the gang ends up trying to murder him.
He alone is the main trial for both the Wrath and Pride chapters of the Book of Eibon.
Toshiori Umesada, one of the 15 20th Seats of the 9th Division (or 20 15th seats, depending on the translation), is highly arrogant and tries to hit on Orihime while she's posing as a new recruit, threatening the similarly disguised Uryu with harsh punishment when he tells him off.
Baraggan, as the God-King of Hueco Mundo, had the power to control time to age everything around him. He was deposed by Aizen and is second in power only to Starrk, another Walking Wasteland. His fraccions therefore have an over-inflated sense of their own importance, share his great arrogance and believe they're much more capable than they truly are. The exceptions are Poww, who needs to be defeated by a captain in Bankai, and Charlotte, who requires Yumichika's Coverblowing Superpower to defeat and seems to be Barragan's genuine Number One fraccion. He's later resurrected by Mayuri to fight an enemy even shinigami captains struggle against.
Xcution thought they could take on the Shinigami captain and lieutenants who spent hundreds of years training simply because they gained a piece of Ichigo's Fullbring. Obviously they are quickly defeated with little difficulty.
Luppi, the guy who replaced Grimmjow as the Sexta Espada for a bit, mocks and looks down on Grimmjow, completely ignorant of how powerful his predecessor was. However, he only replaces Grimmjow because Aizen needed a decoy to distract the shinigami while Orihime was kidnapped, and even then he is defeated by the Hitsugaya. When Aizen reveals the plan and forces Orihime to heal Grimmjow, Grimmjow immediately one-shots Luppi to show the difference in power between them and to reclaim his position as Sexta Espada.
Driscoll Berci thinks that a recently acquired power will enable him to successfully kill the Gotei 13's Captain Commander. The power concerned is the bankai of Yamamoto's lieutenant and he gloats to Yamamoto about killing him. The result? Driscoll's reduced to a pile of ashes.
Excel Saga's eponymous character Excel is extremely confident about her ability to accomplish ACROSS's goal of world domination (and win the heart of Il Palazzo), but fails to make any progress whatsoever in either of those two goals.
In fact, she refuses to acknowledge that Il Palazzo actively dislikes her, sending her falling through the trap door every time.
In the manga their relationship is considerably complex; Il Palazzo's conflicting personalities seem to alternatively hold strange affection towards Excel, or consider her a nuisance. Excel herself is far from stupid, but has overactive imagination, and a habit of acting before thinking. The introduction of Elgala to the story has brought out Excel's responsible, sometimes even tyrannical side (she doesn't know when to quit), and the most recent development has replaced her with a robotic duplicate who is cool, calm and hypercompetent, yet still somehow manages to convey her personality well enough to keep Hyatt and Elgala fooled for several volumes.
This is probably a driving point behind many of the characters in Zatch Bell!. Gash himself somewhat fairly evaluates his own powers, but Kanchomé always brags about how strong he is although he almost never comes through. Most of the early antagonists that Gash faces are like this too, and end up being rudely awakened by Gash and Kiyomaro.
Late manga spoilers: This takes an interesting turn later on, when Kanchomé finally unlocks his true potential during a training arc. He gains several new spells and becomes one of the most powerful demons remaining in the battle, even surpassing Gash in one of their mock fights. This later leads him to a very near Face–Heel Turn however, and soon afterward he's sniped down by the current Big Bad before he can become a real threat.
Kanaria from Rozen Maiden touts herself as the smartest of all of the Maidens. Too bad all her plans seem to fail miserably.
She can be Sun Tzu mixed with Einstein and it wouldn't help if she's still the second (barely) least mature of the maidens.
Patrick Colasour from Mobile Suit Gundam 00, who will proudly boast that he's the champion of mock battles - even as the Gundams take him apart limb by limb. The fact that he still manages to be The Determinator in spite of this, and that he's comic relief that isn't annoying as all get-out, has made him an Ensemble Dark Horse.
By the end of the series he is actually a fairly skilled pilot, though still hopelessly outclassed by the Gundams. He also seems to have gained some humility in the meantime: he no longer boasts about being an awesome pilot, though he does jokingly call himself "invincible" due to his mocking nickname.
Mashymar Cello of Mobile Suit Gundam ZZ started out in this trope, he would remember his awesomeness compared to the plebeians whom he fought and seemed to have multiple dinners with Haman Khan where she would teach him about how he must portray himself and Axis as he was something of a Vanguard, all the while getting his ass handed to him by Judau on a very frequent basis.
In Gundam Build Fighters Try, Kei Karima is a very skilled Gunpla Battler, making it to the Gunpla Battle Nationals twice. However, he really plays up his supposed importance towards his opponents, who usually don't find him that interesting. He also pilots loud and flashy Mobile Armors who get trashed by more agile Mobile Suits.
The eponymous Nora is obsessed with defeating his leash-holder Kazuma via one of his "Ingenious Plans" (TM). Considering he's attempting this against the series' resident Manipulative Bastard... yeah.
Nor does it help that Nora's attempts at strategy usually have flaws visible to an average five-year-old child. One of his Ingenious Plans (TM) in its entirety: 1)Dig a big hole in the ground 2)Make Kazuma walk into it somehow 3)Drop a big rock on his head. Kazuma shows up while Nora's still digging and points out the plan's low probability of success.
Ranma ˝'s Tatewaki Kuno, in his own mind, is a bold samurai with two gorgeous loves, both held in foul thrall by the vile enslaver Ranma Saotome. Despite the fact he consistently defeats the foul cur, the villain continues to hold the two girls from his grasp and allow the man to avoid his fate. One day, the vengeance of Heaven will strike Ranma Saotome down, for that vengeance is slow, but sure. In reality, neither of the girls he chases are interested; one because Kuno is a pervert who likes to spout poetic talk, but is ultimately a braggart intent on groping the life out of her, the other for the same reason and because she is in fact a he, a guy with a Gender Bender curse whom Kuno refuses to admit is the same person as his fictitious "pigtailed girl". (Nabiki Tendo once dumped hot water on girl-Ranma while Kuno was holding her.) And whenever Kuno faces Ranma, it's not Black Magic or cheating that causes Kuno to lose, but the simple fact Ranma has traded a tough upbringing for so much skill in Supernatural Martial Arts that Kuno is thoroughly Overshadowed by Awesome.
Takamura of Hajime No Ippo refers to himself as "ore-sama", which basically means "my great self" and generally thinks to be the greatest in every field when he's not (e.g. women and singing.) In terms of strength, he would be this, if it weren't for the fact that he really is as superhumanly strong as he believes himself to be.
There are hints that he knows his flaws quite well. He simply believes that one must believe to be awesome, if he hopes to become awesome.
Apone from Cowa!! considers very highly of himself.
A common trait among One Piece villains, though a few stand out.
Don Krieg gets special mention because even after getting his entire fleet decimated by a single man, a situation he himself barely survived, he still thinks he's the greatest thing ever.
Wapol sees himself as a great king, when he's really just a spoiled brat.
Bellamy's inability to recognize someone tougher than he is led to one of the more satisfying moments in the series.
Post-Time Skip, he got over it. He is noticeably embarrassed about how he was during this time period. Now, surprisingly enough, he and Luffy respect each other.
Where do we even start with Spandam?!
Hordy Jones is this to the point he believes he and a small army of slaves and pill-popping underlings could take on the entire World Government.
Caesar Clown. He's a logia, so sure, he'd be considered extremely powerful...if it weren't for the fact that he's in the New World, where logias have notoriously short lifespans because they don't get that everyone there has haki and thus can actually hit you. It really says a lot when he, the Big Bad of the Punk Hazard arc, is actually the weakest of the three main villains of the arc. This is mainly due to the fact that unlike other logia users in the series, he relies entirely on his devil fruit power, and has no back up.
Same goes to Caribou, a Logia user who could turn into a energy-draining swamp. He made the mistake of gloating about being a Logia user to Pekoms, a Zoan, and then said Zoan (generally considered the weakest type unless you luck out with one that turns you into a mythical creature or dinosaur) drops him in a single attack. In fact, his purpose (moreso than Ceasar) was to introduce the fact that a Logia needs to be equally badass when their powers are unreliable to survive in the new world.
The title character of Naruto in the early chapters before Character Development kicked in. This is best shown when he asked Iruka why a "great ninja" like himself was in the same group as Sasuke, only to be told that the teams had to be balanced; Sasuke was ranked highest while Naruto was ranked lowest. Although you could say it was almost entirely an act to compensate for feelings of inferiority due spending his entire life being the target of public shaming, hate, and mocking.
The Hidden Star Village, a filler-only village, believe that it can be strong enough to join — or even surpass — the Five Great Shinobi Nations with the power of a chakra meteorite, the "star" in question, and even has the audacity to give its leader the title of "Hoshikage" (a title only given to the leaders of the Five Great Shinobi Nations, who are far beyond the current Hoshikage's Filler Villain level of strength). Unfortunately, this also means that they're willing to make the children of the village train with the "star", thus putting them at risk of health complications and death.
Nora from Witchblade is quite uppity, and stays that way until her demise at the hands of Reina. And she was actually winning that fight too, until she couldn't contain her gloating and trashtalking, then SAT DOWN upon a wounded Reina, completely forgetting that all blade users can make any part of their body a weapon.
Ishizawa in Bakuman。 constantly criticizes manga professionals and thinks that he's a great manga artist, when in fact, he can only draw cutesy sketches of girls. When One Hundred Millionth fails to get a prize from the four chosen for finalists for the Tezuka award, Ishizawa claims that he's better than Mashiro and that Mashiro is dragging Takagi down, despite never having tried anything as ambitious as what Mashiro did, prompting Takagi to punch him. He later gets a series in Chara Kira Magazine, but it's clear that he's nowhere near the main characters' skill.
Naoe Kanetsugu from Sengoku Basara loves to announce his arrival on the battlefield, with a loud declaration of his invincibility, and amazing battle prowess... and always gets swatted away like a common Mook.
Thomas Bester of the Ace Attorney Investigations: Miles Edgeworth manga claims to be a great detective, but he is a Clueless Detective comparable to Gumshoe, and he has only worked on infidelity cases and found lost pets before being hired to protect Randolph Miller's prized painting, "Officers" from a group of Gentleman Thievesbecause he doesn't know enough about art to recognize the painting as a counterfeit.
Subverted in Magi – Labyrinth of Magic. When we first meet Sinbad, he gives his name and various titles and is stunned when Aladdin doesn't recognize him. But as the story progresses, it's clear how important (and dangerous) Sinbad really is and Aladdin was simply oblivious to the outside world.
In Yu-Gi-Oh! GX, all you had to do was check the color of a student's blazer; if it was blue, he likely fit this Trope. With the exceptions of Ryu, Fubuki, Asuka, and usually Manjyome (he had a big ego, but could back it up), almost every Obelisk student was a snob and a serious Miles Gloriosus. In fact, in the second season it was hinted that even if you scored perfect on the entrance exam, you couldn't start there unless you went to some fancy prep school first, implying that a lot of Obelisk students just had rich parents.
Played with in Sore ga Seiyuu!. Ichigo is aware that she's not famous or popular, but she is convinced that she will be.
Shiragami "Cool Beauty" Youko in My Monster Secret is a sexy, Tall, Dark and Handsome expert in love. At least, if she tells you that, just quietly nod in agreement and don't tell her that… she's not. Or find a roundabout way to say it.