Cacofonix, the meaningfully named bard from Astérix. His bravado makes him the perfect unwitting weapon against the Romans, but usually he's just made to shut up with varying degrees of force. His moment to shine came when Vitalstatistix's nephew Justforkix was being held by Normans who wanted to learn the meaning of fear. Cacofonix's singing was so bad they became scared for the first times in their lives.
In one story, a newcomer to the village has called an election as he has a (tenuous) claim on being chief, so the current chief sends Cacofonix, as the person he most trusted to vote for him, to spy on the others to find out who they'd vote for. Cacofonix returns with the data, and a black eye given to him by Caustic Critic Fulliautomatix, who thought he was going to sing. The chief attempts to comfort him by saying that he appreciates his music, so Cacofonix, obviously very excited to have someone to play to, starts playing him a new song he wrote. The chief starts screaming in agony and begging him to leave, so Cacofonix storms out, announcing he's changing his vote.
Jack from Jack of Fables is a rare example of a main character being a Small Name Big Ego. He frequently embellishes himself while narrating; for example, in the beginning, when he recapped the events of Fables, he made it look as though he was the Big Damn Hero of the Battle of Fabletown when he really just played a minor role, and failed at it, to boot.
Turned on its side, the more popular one is with the Mundanes, the easier it is to survive. (That's the current theory, anyway.) Jack scams his way into making movies about his past adventures and literally makes his own ego come true. He loses all his cash and friends eventually, of course, but now is nearly (nearly) immortal. Although a later issue in his own series briefly showed a newspaper title indicating the popularity of Jack's films were starting to plummet.
Crackerjack from Astro City is a variation. He is both highly skilled and truly heroic, but there is no amount of skill that can back up all that talk...
Rat from Pearls Before Swine has a very high opinion of himself and a low opinion of everyone else. While Pig follows this rather blindly, the others don't.
Earl Slackmozer from Knights of the Dinner Table, who thinks having had modules published by Hard 8 makes him the greatest gamemaster in Muncie. His condescension towards to BA is astounding.
Guy Gardner from Green Lantern is constantly lamenting the fact that he is not the primary Lantern of Earth's sector, and bad-mouths Hal Jordan, Kyle Rayner and John Stewart any chance he gets. There is a tradition beginning with Keith Giffen, J.M. DeMatteis and Kevin Maguire's first issue of Justice League International of Guy demanding to be instated leader of any new incarnation of the League, for reasons obvious to no-one but himself.
The infamous 24 Hours story from the beginning of The Sandman started by introducing a waitress named Bette who, unbeknownst to everyone else, has written numerous stories, most of them about her customers at the diner. Bette figures someday she'll send the stories out to be published, become famous, and all the famous talk show hosts and critics will marvel at her depiction of small-town life. However, while we are never shown these stories, the narration states that all of them end happily, and some of them have her pairing up two young lesbians with "fine young men" because she considers what they do is "a sin." (But the couple themselves don't come off much better. It's eventually revealed to be a relationship that's turned emotionally and physically abusive.) Added that some of her tales involve her ex-husband and her convict son coming back to her, it's obvious that Bette's stories are self-indulgent garbage meant to give her an escape from her crappy and boring life, and by the issue's gruesome end, it's obvious she knows next to nothing about her customers.
Cat Grant from the Superman and Supergirl books thinks she is the center of the universe (she isn't), and in Supergirl (Rebirth) she believes that several train hijackers were after her (they weren't).
At the very first issue, the Penguin asks his henchmen to share a new word they have learned ("because being a criminal doesn't mean being dumb"). This patronizing attitude is worsened because the Penguin doesn't know what a word means, so he lies to them and makes it up. One of the henchmen dared to complain...
At Batman Adventures Vol 2, a subplot for issues 1 to 13 is the Penguin winning Gotham's election for Mayor..0 but Batman discovers that it is another revenge scheme by the Clock King to ruin (ex) Mayor Hill's life... the point is that the Penguin really believed that the people liked him and truly voted for him (he was sixth)... then we have this resign speech:
Penguin: So I resign. You don't get Oswald Cobblepot to kick around anymore!... At least not until the fall election, you've seen what I can do as Mayor, Gotham City. When the time comes, I'm sure to come back in a landslide!!... Now, NO further questions you vultures! I'm done with you!
Temple Fugate (the future Clock King) cannot understand why Counselor Hill has not learned his name yet, even when they have shared the same train each day for one year, seven months and thirteen days. This is one of the signals of Fugate's arrogance: he believes he can do everything in the most efficient way.