This post makes me ridiculously happy, because I always love hearing about characters who fit this trope in canons with which I have only passing familiarity!
I generally define Badass Normal characters as those who, in canons with some sort of superpowers (whether inherent, learnable, or creatable), either don't or can't acquire them but still manage to hold their own in a crisis, especially in ways that the powered characters don't expect or can't replicate. Their normalness should be a defining characteristic, often in ways that some (usually the villains) initially regard as a flaw. Some of my most beloved examples of the trope are:
Saten Ruiko (A Certain Scientific Railgun) - In a city literally devoted to making superpowered kids, where the top-ranked Level 5s are effectively one-person armies in terms of raw power, Ruiko is a completely unpowered Level 0. Even though she wishes she could have powers, too, the canon makes her lack of powers both a disadvantage and a saving grace. Specifically, in a situation where the villain has created a sonic weapon that cripples all of the superpowered characters, Ruiko is the only one unaffected by the noise, and so she's the only one who has the ability to destroy the weapon -- by grabbing a baseball bat and beating it to smithereens.
Kajiki Yumi (Saki) - In this mahjong anime, most of the characters have some sort of crazy luck or power that affects the outcome of the games they play. Yumi is one of the handful of normal ones with no power or ability beyond incredibly good mahjong skills, and she holds her own at the table against two characters who are described as demons capable of crushing their opponents single-handed. Even though she doesn't win, the other girls respect her skill, and she shows up later to help the winning team train for the national-level competition.
Kokutou Mikiya (Kara no Kyoukai) - A totally average (but caring and kind) guy who falls in love with Shiki, a superpowered girl who has the ability to see the invisible fault lines that mark everything in existence, and can cut along those lines to kill or destroy anything, from flowers to entire buildings to ghosts to magical spells. Other characters remark on how absurdly normal Mikiya is, but when Shiki's in danger he's willing to face down crazed mages and serial killers in an effort to protect her, and succeeds mostly because he's just that devoted to her.
(That said, I don't know enough about Homestuck to make the call on those characters, but Vimes definitely counts in my book.)
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I generally define Badass Normal characters as those who, in canons with some sort of superpowers (whether inherent, learnable, or creatable), either don't or can't acquire them but still manage to hold their own in a crisis, especially in ways that the powered characters don't expect or can't replicate. Their normalness should be a defining characteristic, often in ways that some (usually the villains) initially regard as a flaw. Some of my most beloved examples of the trope are:
Saten Ruiko (A Certain Scientific Railgun) - In a city literally devoted to making superpowered kids, where the top-ranked Level 5s are effectively one-person armies in terms of raw power, Ruiko is a completely unpowered Level 0. Even though she wishes she could have powers, too, the canon makes her lack of powers both a disadvantage and a saving grace. Specifically, in a situation where the villain has created a sonic weapon that cripples all of the superpowered characters, Ruiko is the only one unaffected by the noise, and so she's the only one who has the ability to destroy the weapon -- by grabbing a baseball bat and beating it to smithereens.
Kajiki Yumi (Saki) - In this mahjong anime, most of the characters have some sort of crazy luck or power that affects the outcome of the games they play. Yumi is one of the handful of normal ones with no power or ability beyond incredibly good mahjong skills, and she holds her own at the table against two characters who are described as demons capable of crushing their opponents single-handed. Even though she doesn't win, the other girls respect her skill, and she shows up later to help the winning team train for the national-level competition.
Kokutou Mikiya (Kara no Kyoukai) - A totally average (but caring and kind) guy who falls in love with Shiki, a superpowered girl who has the ability to see the invisible fault lines that mark everything in existence, and can cut along those lines to kill or destroy anything, from flowers to entire buildings to ghosts to magical spells. Other characters remark on how absurdly normal Mikiya is, but when Shiki's in danger he's willing to face down crazed mages and serial killers in an effort to protect her, and succeeds mostly because he's just that devoted to her.
(That said, I don't know enough about Homestuck to make the call on those characters, but Vimes definitely counts in my book.)