Badass Bookworm/Fan Works

Examples of Badass Bookworms in Fan Works include:

Works based on Harry Potter

Dumbledore's Army and the Year of Darkness shows just what happens when you get the Ravenclaws seriously riled up.
Harry in Harry Potter and the Invincible Technomage. Not only is he on his way towards being as brilliant as his adopted father Tony Stark, he also gets regular physical training from Hell by Captain America.
Hermione Granger in The Arithmancer is the canon Hermione cubed. She passes her Arithmancy NEWT before fifth year and starts working on a Mastery in her fifth. She invents spells that terrify people on both sides of the war. She's a published researcher into arcane magics before she's past her fourth year. She essentially invents Magitek. She comes up with the way to kill Voldemort at the end -- and she battles Bellatrix Lestrange one-on-one while at a severe disadvantage but still triumphs. After the Battle for Hogwarts is over, she's told that she's probably the most accomplished and deadly fighter in all of Magical Britain.

Other works

The Second Try has Shinji and Asuka becoming milder examples of this trope by necessity, since they had to accumulate and learn the sum total of human knowledge after they're left being the only two humans left alive on Earth, and are basically pigeonholed into being a civilization of two.
In the Pokémon story Brave New World, the first new addition to Team Aurabolt is a fat basement-dweller Squirtle with tenuous grasp on the difference between fiction and reality. He starts things off by pounding the crap out of the protagonist (who has already defeated entire armies) via Confusion Fu, proceeds to predict half the plot turns in the story, defeats homicidal demons via children's card games and a manifestation of the futility of life using nothing but logic, stores entire arsenals in his shell, holds his own in direct combat, and generally embodies Crazy Prepared and Crazy Awesome.
The protagonist/narrator of Travels Through Azeroth and Outland fits this description.
Yuuki Nagato of Suzumiya Haruhi no Seitenkan is even more Badass than the original Yuki Nagato.
Tara "Green Shield" Strong from DC Nation. Yes, she is a Snark Knight first and foremost, but this is someone who has a Masters at 19, is getting her M.D. by apprenticing under Doctor Mid-Nite, and got her abilities by playing Professor Guinea Pig on herself to try and prevent her crooked boss from taking credit for her work. She's even studying alchemy in order to better keep up with the magical trouble the JSA attracts.
John in With Strings Attached qualifies. In Real Life he was a voracious reader, not to mention a songwriting genius. In Strings, he's transformed into a guy who can fly and lift half a ton (though not at the same time) and given a magical charm that makes him powerful enough to lift a river. Not that he actually wants to do anything to you—unless you fuck with him or the others.
- Paul and George probably qualify as well.

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