Regal Pinion's "Clockwork Seraph" is this. As well as "Secret Keys". The song "More Grim Grimoire" can be seen as a deconstruction since he slowly delves into lamenting that he can't improve since there is no one better than himself.
The Binary Star song "Honest Expression" is largely a reaction to this trope; an extended tirade about how everybody who makes Boastful Rap songs is a poser who is killing hip-hop.
Knuckles the Echidna gets into the act in Sonic Adventure, trying to convince us that he didn't chuckle in every single one of his Sonic 3 appearances, or that he has any form of visible musculature.
Most of HP Baxxter's song lyrics have something to do with his superiority as a rapper.
Scooter do have a lot of haters, especially since they started relying on squeaky voiced choruses all the time. So you'll have an odd situation where in the verses HP is rapping about his brilliance and originality and the chorus is a squeaky voiced rendition of a well known song. Then again, this is quite common in classic hip hop.
Jimmy's rap from Dreamgirls, which immediately leads to the firing of Jimmy.
Look Pimpin from MadWorld, as sung by the final boss, The Black Baron (stop staring). There's also You Don't Know Me, which was based around the lady bosses (Elise and Rin-Rin). Not based on anyone, but still a boast of power, is Ain't That Funny, the Great Wall Street theme.
Honestly, pretty much 95% of Anarchy Reings' soundtrack consists of rap that proclaims the singer's superiority, usually in battle. Given that they are battle themes, this is not surprising. Jaw? Lights Out? Play My Ass Off? Kill Em All? Pick pretty much any song in the soundtrack, it's significantly more likely to be a boastful rap than anything else.
Even the poster boys of Wangst aren't exempt from this. See Linkin Park's "Step Up" and "High Voltage". The band's rapper continues this trend with Fort Minor's "Remember the Name".
Lupe Fiasco's "Superstar" was a surprising deconstruction of this trope. Though he wasn't parodying those who boast, it was definitely more about the insecurities and loneliness that come from 'gangsta' celebrity rather than the perks, fame, and money.
iCarly during the party scenes of iParty with Victorious is a good example of this trope. However, Sam and Rex are the only characters that don't make Tupac roll over in his grave.
Subverted by Robbie who gets knocked unconscious by an angry crowd member before he can make a presumably poor attempt of a Boastful Rap.
Chris Brown's "Look at Me Now".
DJ Khaled's All I Do Is Win might be one of the straightest examples to hit the charts in recent years. Features guest spots from T-Pain, Ludacris, Snoop Dogg, and Rick Ross, and every single one of them is attempting to one-up each other.
Mickey Avalon's My Dick is all about the comparative size of the artist's genitals.
With the exception of "We Are One (Ole Ola)", the 2014 World Cup theme, name one Pitbull song that doesn't fit this trope to a T.
"Thrift Shop" by Macklemore and Ryan Lewis is an amusing example that still plays the trope straight. Most boastful raps focus on how wealthy and stylish the rapper is. This song brags about how great the rapper looks despite having no money and "wearing your granddad's clothes."
The Black Eyed Peas do this sometimes, like "Boom Boom Pow" and "Imma Be." Fergie does this too ("Fergalicious," anyone?).
Don McCloskey's "Return of the Freak MC" starts off with him mock-complaining about how folk-singers brag about how much money they have, how many banjos they play, before launching into a song about how broke AND awesome he is.
"Remember the Name" by Fort Minor (Mike Shinoda and Styles of Beyond working together), in which each artist gets two verses. They proceed to describe themselves in a distinctly self-satisfied fashion.
Cher Lloyd's "Swagger Jagger". A white British girl rapping about how awesome she is and how everyone's trying to jack her swag, to the tune of "Oh My Darling, Clementine". It's exactly as ridiculous as it sounds.
While most of Bad Lip Reading's "(Rockin') All Nite Long" is silly like their other works, Wiz Khalifa lays one straight line that stands out.
"'Bout to get raw, bells gotta ring, I'm a alchemist, the beat is my base metal..."
I'm down with Bill Gates, I call him "Money" for short I phone him up at home and I make him do my tech support
50 Cent did "Window Shopper" with a video that featured super-imposed pricetags on every piece of product placement. Lily Allen then did "Nan You're A Window Shopper" which reversed and parodied the original.
"Gangnam Style" by PSY. The narrator brags about his luxurious life style, while the video reveals the inaccuracies. For example, PSY appears to be lounging on beach, but he's actually on a playground; he brags about his wealth while sitting onthe toilet, and so on.
Gangnam is a wealthy part of Seoul, South Korea. The main line is "Oppan [Big brother is] Gangnam Style" - the song is effectively from the viewpoint of a man who went to Gangnam and now thinks he's hot stuff.
The Flobots' "Handlebars" is a deconstruction of boastful rap, starting with childlike bragging ("I can ride my bike with no handlebars") and culminating in some pretty scary stuff ("I can end the planet in a holocaust").
Tinie Tempah's "Pass Out" is half straight example, half Affectionate Parody. The hook is standard if arguably lame Boastful Rap about partying and drinking and getting all the women, but the verses contain bizarre, uncool boasts like "I got so many clothes I keep them in my aunt's house" and "I'm pissed I never got to fly on a Concorde / I been Southampton but I've never been to Scunthorpe". (Note: for Americans unsure about those English towns, know that they are both desperately uncool.)
At one point, Tavros attempts to troll Dave by performing a Boastful Rap ("'Cause I'm your bully, and you're not in charge"), but unintentionally keeps making it homoerotic, much to Tavros's chagain.
On Whose Line Is It Anyway? Wayne Brady and Brad Sherwood once did a rap song about being an astronaut. "We're gonna blast off out of this place / And we're gonna drag your butt to outer space! And if you do not like it I do not care / Because I told you once, I'm breathing BOTTLED AIR!"
There's Romans think they're minted, but they ain't rich like me! You can't call yourself loaded till you can buy an army! Ran Rome with Pompey and Caesar, they're more famous than me, But I'm the world's richest geezer, there's no-one richer than me!
The Digital Underground song "The Humpty Dance" is a humorous example if not an outright parody.
"Deadpool - A Blurred Lines Parody", done by D Piddy, basically turns that song into one of these, centered on the titular character.
Pokémon: The Mew-sical has Brock's song, which is a rap about how he's a chick magnet using Pokemon-themed words. it's... not entirely accurate.
Die Antwoord has "Rich Bitch," which (like most of the group's material) plays as an Affectionate Parody of the genre as Yo-Landi Vi$$er boasts about, among other things, eating sandwiches with thickly spread Nutella.