In the Marvel vs. DCCrisis Crossover, Batman said that if he fought Captain America, the fight would go either way. Therefore Batman's badassitude equals Captain America's. Kurt Busiek side-stepped the fight entirely in JLA-Avengers, although according to him, Cap would have won after one of the longest comic book fights in history.
Alfred is generally considered the only being capable of defeating Batman in-universe, as his Servile Snarker and Team Mom.
Spider-Man is known by many fans as the poster boy for Badass when his loved ones are in danger, especially Mary Jane and Aunt May. Even against Heralds of Galactus or Juggernaunt, he still beats them down and wins.
Only by having power over adamantium (Magneto) can you really stop Wolverine for a long while, which reminds him why he hangs out with the X-Men at all... it's to gain even more badass aura without having to kill every villain once the villain's stamina runs out and Wolverine's regeneration doesn't!
Rorschach. He's not locked in here with you people. You're locked in here with Rorschach!
Rorschach once ate an entire seven-layer cake all by himself, then killed the stripper inside for being a whore. Add many more to that effect, usually involving breaking some specific number of fingers and killing dogs.
When nobody was looking, Rorschach broke five people's fingers. That's as many as five tens. And that's terrible.
Jamie Madrox is a relatively unknown superhero. His power is to make duplicates of himself. On the occasion that he got stranded in the Arctic, what did he do? Did he make duplicates of himself and cuddle together for warmth? NO. He duplicated himself, then killed the clone and ate it.
And it wasn't just some mindless duplicate either. Each clone Madrox makes has all of his memories, abilities, and free will. Madrox killed and ate himself to stay alive.
Captain America is on this page for roughly the same reasons as Batman. Despite being only a normal human superhero in peak condition, the Cap has gone on to defeat villains and heroes alike whose strength, speed, and powers greatly exceed his own. He's able to battle toe-to-toe with the Hulk, and in the Ultimates comic, he defeated an enormous Giant Man with his bare hands (just to name a few examples). Captain America's feats, much like Batman's, can either be seen as the very peak of badass and cool, or over-the-top bad writing that borders on God Moding and writer bias.
During the Nineties, there was a period where Cap was missing and presumed dead, and a bystander asked the other Avengers what was so great about Cap. Hercules replied that in Olympus, they consider Zeus to be the paragon of wisdom, Hermes for speed, but they measure courage... by Captain America.
So Thanos the Mad Titan has won. He has collected all of the Infinity Gems and created the Infinity Gauntlet. He has wiped out half of the population of the UNIVERSE with a thought. He's toyed around with super heroes, defeated every cosmic being imaginable and he reigns supreme. You have a plan to take him out, but you need someone to distract him. Captain America calmly walks up in Thanos's face and dares to take him on. Plan doesn't work, but I'm sure this is a Crowning Moment of Awesome
To clarify: In a group of super heroes where admission requires a UNIQUE superpower at a level that can put you on par with the greatest of the Silver Age, Karate Kid is a normal human being. His superpower? "I can put Superboy in a headlock." And he CAN.
Karate Kid lifted the entire Sydney Opera House from two thousand miles of ice, with his bare hands. With nothing but "focus."
Sgt. Frank Rock is more badass than Batman. Seriously, there was voting and everything.
Squirrel Girl. Pick a character, pick any character, even some cosmic super teams, against Squirrel Girl, and Squirrel Girl will be the accepted winner. Unicron and Galactus versus Squirrel Girl? Squirrel Girl.
Squirrel Girl versus Chuck Norris? Same result but Chuck Norris wins and then Squirrel Girl wins because she has one big advantage; being Squirrel Girl.
Deadpool thinks she's the greatest threat in the marvel universe.
Squirrel Girl Vs. Batman? Batman could defeat Squirrel Girl with Prep Time, but Squirrel Girl wins because she doesn't need prep time to beat Batman.
The world needs a real Squirrel Girl, so whenever someone gets too pompous, they have to lose to an army of squirrels.
Deadpool can beat anyone, except Squirrel Girl, while talking to the audience and being an asshat all the way.
On some debate forums May Parker and Ma Kent are sometimes referred to as the most powerful beings in their respective universes on the argument that their power has never shown an upper limit. This is usually brought up when someone Fails Logic Forever during a a debate.
The Midnighter is a literal version of this. His superpower is that he doesn't lose fights. Ever. Seriously, Midnighter wins every fight, whether he's actually in it or not unless he's fighting Captain "Why Don't You Try That Trick On Me" Atom, at which point Midnighter (and Apollo, for that matter) becomes just another super-powered punching bag.
He also beat HIV in 6 weeks, and doesn't have the common cold for more than a couple of minutes. His immune system is as badass as he is.
Give Paco an opponent and a stick to beat them with and he will fuck their shit up. Anyone, ever.
Nick Fury in Secret Warriors: Surrounded by HAMMER agents and ordered to surrender, Fury replies, "Son, you got about five seconds before I take that gun away from you and beat you to death with it." The HAMMER agents give up.
Rex the Wonder Dog once nuked a T. Rex, has had a successful career as a newspaper photographer, knows how to operate heavy machinery and vehicles, can fish, operate a parachute, and rope cattle. Then, after he did all that, he gained the ability to talk and became a wizard. One might even go so far as to say that is is truly top dog.
Fantastic Four are considered in-universe as an example of this trope. Despite not being anything close to the most powerful superheroes in the Marvel universe, they are still always the automatic go-to guys for cosmic-level threats, due to their innate ability to just awesome their way to victory, no matter how insanely powerful the threat may be.
In one occasion, Reed Richards stumbled on some alien invaders, tried to reason with them, presented himself as "Reed Richards of the Fantastic Four", and then looked at them running away in terror.
Luke Cage gets some of this, owing largely to the infamous instance of him invading Latveria and attacking Doctor Doom on his lonesome because Doom owed him money (200 dollars). Several quotes from the issue are quite memetic by their own right, such as Luke's demand upon busting into the throne room: "Where's my money, honey?"
The Transformers: In the marvel comics it was Buzzsaw. He was a yellow Laserbeak, meaning he was one of the smallest Transformers ever, but in the marvel comics, he was very effective, taking down several Autobots, but most prominently, he beat Omega Supreme, one of the largest Autobots in the series, in one shot. The Captions on TFwiki are an indication of how badass he is.
DC Comics' own "F-Sharp Bell", Rot Lop Fan. For a character who has only made three appearances in the entire history of the Green Lantern franchise, he's one of the most popular Green Lanterns. The two appearances after his origin story depicts him performing amazingly badass deeds (how do you take down a diamond-bodied villain whose body naturally deflects green light rays? Hit him with sound...), hence his ascension to Memetic Badass status.
Judge Dredd. When the Face of Fear kills anyone who gazes into it, Dredd is the only one it can't kill. Fear is not so resistant to the Fist of Dredd. Also, he once got an entire army to back down by simply appearing on a comm screen.
The Joker is a Memetic Badass in-universe. As the Trickster once put it: "When villains want to scare each other, they tell Joker stories."