Leigh (Laurie Zimmer) in John Carpenter's original Assault on Precinct 13 (1976). She starts out as just a secretary in a police station but becomes an action girl when the nearly-abandoned station is under siege by a street gang during the night and fights them off along with the lone policeman and two convicts. She keeps her cool especially in comparison to the other secretary who panics.
Tony assembles the Mark 42 around Pepper in one scene, which she then uses to save Tony. Pepper also gets injected with Extremis later, allowing her to save Tony from the similarly super-powered Killian.
To avoid spoilers Eve from Skyfall is a clear cut action girl-a badass driver, a sniper,and in the middle of a gun battle graps a pistol and takes on a team of assassins lead by the big bad, all without breaking a sweat.
Johnny Mnemonic has Jane, a female cyborg bodyguard. She's not as Bad Ass as Molly Millions in the original story, but this was probably due to the limits of cinema at the time.
In Last Action Hero, Slater's daughter is one of these, and at first it's played for laughs by subverting the Distressed Damsel — she's screaming mock-hysterically as she kills the mook sent to take care of her. But it's also deconstructed a bit when Slater mentions that she spent her prom night alone in her room, field-stripping an AK-47.
Arguably, Gipsy Danger. Gipsy has only been referred to with feminine pronouns, "she" and "her". Not to mention Pentecost at one point referred to her as "the lady". Her form is also more feminine with a large chest and a thin waist widening to thick thigh muscles, compared to the other Jaegers (Striker Eureka being a male brawler, Crimson Typhoon an artful dodging basketball player and Cherno Alpha a walking tank).
Red Dawn 1984. Teenaged girls Toni and Erica, who subvert the usual trope by being too rugged up in the Colorado winter to be much fanservice. After the Ragtag Bunch of Misfits kill their first Dirty Communists, they state flat out that the guys can do their own washing up. We later see them blasting away in ambushes and using their feminine wiles to get bombs into places where the Russians really don't want them going off.
Interesting little semi-subversion in Red Eye. Rachel McAdams' character is manipulated, abused, and (metaphorically) raped by Cillian Murphy's Magnificent Bastard, and eventually she decides to man up (for want of a better term) and brutalize him with a pen, a shoe, and a field hockey stick. She does pretty well (or at least, well enough not to be a Faux Action Girl), but she still needs the help of Daddy Brian Cox, who also mans up just in time.
In the third Riddick movie, Dahl (Katee Sackhoff) is a seasoned mercenary and sniper, and beats up an attempted rapist.
Princess Leia Organa from Star Wars often switches in and out of the Action Girl role. She must have got it from her mother, Padme Amidala, who is, incidentally, the best shot with a blaster in the entire series.
Babydoll, Sweet Pea, Rocket, Blondie, and Amber from Sucker Punch.
Selena in 28 Days Later has this kind of scheme going on. Since 28 Days Later is on the cynical end of the Sliding Scale of Idealism Versus Cynicism, she may be badass and violent, but she's still just a rather athletic chemist with a machete. It's therefore understandable when she gets a bit Chickified toward the end when surrounded by a bunch of soldiers.
Yukio for the most part but even Mariko gets in on the action as well in The Wolverine.
Films and creators in general:
Action Girls were not common in early movies, as the true form usually requires convincing hand-to-hand combat skills. However, a female character in a Western or Pirate movie could get away with the role. Maureen O'Hara is probably the most famous. She had a powerful screen personality, great acting skills, and an ungodly beauty that could carry any part. She also always looked to be having enormous fun whenever she got in a swordfight, most particularly in Against All Flags (as a Pirate Girl) and At Sword's Point (as the daughter of one of The Three Musketeers!).
In Aliens, Ellen Ripley was slowly converted from a Final Girl into an early example of the Action Girl. Her performance earned her an oscar nomination and the number 8 spot on the AFI's Greatest Heroes list. She frequently appears on lists of the best female Heroes. We also see Vasquez, a butch action girl.
In the first two Terminator films, Sarah Connor grows from Distressed Damsel to one of the most badass heroines of all time, perhaps the only other that can truly stand beside Ellen Ripley.
Mace in Strange Days. It pretty much takes an entire police SWAT team to kick her ass. Justified in that she's a professional bodyguard, whom you'd reasonably expect to be able to kick someone's ass if necessary.
Most recently, in Avatar we have Trudy Chacón who goes out all guns blazing, the Na'vi princess Neytiri and — while not quite an Action Girl in this film — Sigourney Weaver's Dr. Grace Augustine, who's still no Distressed Damsel.
Many Kung Fu movies. In particular, characters played by Cheng Pei Pei (60s and 70s), Brigitte Lin, Michelle Yeoh (both 80s and 90s; coincidentally, she played the aforementioned Wai Lin), and now Zhang Ziyi.
Yeoh, Zhang and Cheng came together as Shu-lien, Jen, and Jade Fox of Crouching Tiger, Hidden Dragon. The sequence in the bar is FANTASTIC, as well as the fight between Shu and the rebel Jen.
In the 1980s, the so-called "girls with guns" subgenre took off in Hong Kong action cinema. Despite its name, the "guns" in question were usually quickly discarded in favor of bareknuckle brawling, thus making more straightforward Action Girl stars out of Michelle Yeoh, Cynthia Khan, YukariOshima and Cynthia Rothrock. The latter two were actual martial artists (and Oshima was also a stuntwoman), making this borderline Truth in Television.
Ukrainian model/actress Milla Jovovich frequently plays Action Girls. She has the attractiveness to get by in Hollywood, and the lean, rangy body of a female athlete.
Joan of Arc, The Messenger: The Story of Joan of Arc.
Mothra has been the Kaiju version of an action girl since her first appearance, and is arguably one of the most successful ones ever, starring in her own film series, and appearing frequently in the Godzilla franchise. In the case of the latter, she's one of the few monsters to ever defeat Godzilla (and did it with no fancy powers), is willing to stand up to King Ghidorah in her larva form, and usually takes on the role of The Smart Guy and Only Sane Man during team-ups.
Akane Yashiro from Godzilla Against Mechagodzilla, the Ace Pilot of the Millenium Era Mechagodzilla, and one of the few humans with the guts to take on the King of the Monsters one-on-one.