Nerd Action Hero

When a character is primarily a Nerd (or possibly Geek), but still manages to pull off feats of Action Heroism, then he (or she) is a Nerd Action Hero.

Sometimes this is the result of Character Development, where the character starts out as a Nerd but over time develops heroic skills. In other cases the character is a Hidden Badass

Sometimes a Nerd Action Hero may be paired with an Action Girl, and aforementioned Character Development may occur as a result of their interaction.

There is an overlap with Badass Bookworm, but many of those are Badass first and bookworm only as a bonus. There can also be an overlap with Science Hero, but a Nerd Action Hero more tends to do ordinary Action Hero things (shooting, fighting, jumping, etc.) when the action starts.

Anime

 * Yomiko Readman of Read or Die.
 * Throughout the Haruhi Suzumiya series, due to all the strange things that happen to Kyon, he develops into this. However, after a while, he leaves things to Yuki. After the Disappearance (Vanishment) movie, though, Kyon has the ability to bargain with aliens that have godlike powers.

Comics

 * Valierie from Danger Girl is Nerd first and Action Girl second, so she qualifies. Abbey, on the other hand, is Action Girl first and bookworm second.
 * Mr. Fantasic of Fantastic Four also qualifies, although it may be Depending On the Writer.

Film

 * The main protagonist in The Librarian starts out as an overage student who doesn't know when it's time to stop accumulating degrees and get a job instead — quite nerdy. Then he gets a job which requires him to be the hero.
 * Indiana Jones would probably appear as this to one of his students or neighbours, as college professor = nerd, but since we in the audience mostly get to see him in the field he probably doesn't qualify.
 * Milo Thatch in  ~Atlantis: The Lost Empire~  starts out as an out-and-out nerd, but mans up and leads the final assault on the bad guys.
 * All the main characters from The Last Lovecraft qualify, but top marks must go to Paul, who leads the bad-guys away to save the two remaining heroes, gets knocked out, backflips out of a window and then runs across the desert with two broken arms, before asking for some dynamite be shoved down his pants so he doesn't feel left out.

Literature

 * Neal Stephenson is fond of these:
 * Sangamon Taylor in Zodiac is an analytical chemist who spends most of his time (most of the words in the book, anyway) looking for traces of compounds with covalent chlorine (and other toxins), and talking to people about these issues. He also engages in a lot of spy-like activities (covert intelligence gathering, sabotage, misdirection, etc.) before the action gets really hot.
 * Hiro Protagonist in Snow Crash is a programmer who in real life is pretty close to broke (after having failed his pizza delivery job) and lives in a self storage facility, although he also own a pretty large chunk of prime real-estate in cyberspace (think IP address block) on account of having been one of the guys who created it. As it happens, he is also the greatest swordfighter in the world (though he mostly gets to demonstrate it in cyberspace), and turn out to be good at other acts of ActionHeroism as well.
 * Randy Waterhouse in Cryptonomicon spends most of the book as a pretty ordinary computer programmer, even though the fact that much of his company's business is in the Philippines brings some travel. At the end however, develops some Badass, and comes out as a fully capable action hero just in time for the Final Battle.
 * Professor William Race of Temple by Matthew Reilly definitely qualifies.

Live Action TV

 * Chuck is a textbook example. Complete with his Action Girl girlfriend.
 * Daniel Jackson of Stargate SG 1 eventually developed into this.
 * As did Rodney McKay of Stargate Atlantis, who started out ejecting the clip from his gun while attempting to fire it to carrying and effectively wielding a P-90 and acting just as physically competent as Sheppard, the Lt. Colonel team leader.

Video Games

 * Ernie Eaglebeak of The Spellcasting Series. He's got an atomic dragon and a sea monster on his tally, plus, you know, saving the world a few times.

Web Original

 * The Angry Video Game Nerd may be a stereotypical geek, but when he has to deal with entities that threaten his life, he sure knows how to use a light gun.
 * Jericho of the Whateley Universe is Black and Nerdy. He's an inventor at Super Hero School Whateley Academy. He's working on power armor designed to help firemen and emergency medical technicians in combat areas. But he's also on a training team with Eldritch, Diamondback and Razorback. This training team is widely felt to be the scariest team on campus.