The theme of Ben Folds song "There's Always Someone Cooler Than You":
...and you won't Even know that they're not sizing you up They know your mom fucked you up Or maybe let you watch too much TV
There's a song called "I'm Awesome" by Spose. It's completely counterpoint to the title because the guy is describing how much of a loser he is and yet still thinks he's the greatest human being alive.
The protagonist of English novelty song "Don Alfonso" (released by Mike Oldfield on his second single) continuously boasts about his abilities as a toreador ("I kill bulls by the score/ And sometimes more"). In the end, when he faces a real bull onto the arena, he instantly chickens out and gets rammed into his, well, posterior.
Throckmorton P. Gildersleeve on Fibber McGee and Molly was a pompous gasbag, although once the character moved to his own spinoff show these tendencies were downplayed.
Then there was Mrs. Uppington, a rich society matron who Fibber frequently traded barbs with.
Denis King on Hello Cheeky, although subverted in that he was genuinely competent as a pianist. However, he gets the fewest acting parts and is the worst actor, yet keeps insisting that he's the real star of the show.
In one episode, he complains about the others picking on him, and goes to see a psychiatrist. His philosophy is more or less summed up in their dialogue:
Denis: Doctor, I'm worried! I can't sing, I can't dance, I can't play the piano...
Psychiatrist: Well, why don't you quit showbusiness?
Denis: I can't, I'm a star!
Parodied by San Francisco Giants broadcaster Duane Kuiper who managed in 3,700+ at bats to hit a single home-run. He jokingly has milked this for all its worth to the point of it becoming a Running Gag among the fan base
He had a single t-shirt printed up with Official Duane Kuiper Home Run T-shirt. A recreation of this shirt can be purchased from The City Graphics
In 2014 The Giants had as a give away an Official Duane Kuiper Home Run Bobble head. Prior to the broadcast of the game a short faux tongue and cheek documentary aired about the event; complete with his grown children showing off all his memorabilia from that game and complaining about how often they have had to hear the story.
Excessively Righteous Blossom in Exalted. Because awesomeness is required to be an Exalt, he actually isn't too bad — it's just that he thinks his most impressive gifts are in areas that he isn't actually any good at, while neglecting his very real skills.
Another example would be the stunningly inept Lunar known as Ten Stripes, whose total lack of talent in social manipulation is matched only by her pride in the social manipulation skills she does not in fact have.
The Tau Empire of Warhammer 40,000. They like to think they are a Superior Species with super-advanced technology and their "The Greater Good" ideology, and are incredibly confident in their manifest destiny to unite the stars under their banner. They're really dangerously overstating their race's potential; they became a space-faring race only relatively recently, their empire is relatively small and weak, they are utterly naive and completely unaware of the kind of Crapsack Galaxy they inhabit and what nightmares lurk in it, and every encounter they have had with the galaxy's major players (the Imperium of Man, the Tyranids, the Orks, the Dark Eldar and the Necrons) mostly resulted in the Tau getting their asses kicked until another race intervened, or they manage to pull a win through sheer blind luck. The fandom generally views them as The Scrappy for this reason.
While Strong Bad from Homestar Runner is actually one of the more rational and intelligent ones in the cast, this doesn't say much - he falls squarely into this trope. He is convinced he is cool, handsome and painfully seductive, although his actual track record makes it fairly clear he is somewhat chubby and not very attractive.