Extraordinarily Empowered Girl

There is a niche between the ordinarily powered heroine and the superpowered Supergirl heroine. She has a little extra somethin' most humans don't, but is nowhere near The Cape (trope) country.

She is independent and strong willed, but vulnerable. Her little extra somethin' isn't powerful enough that she won't have to use her brains to solve a problem, but she can occasionally call on that somethin' for a solution most people couldn't use.

She is essentially a fantastic expression of "Girl Power", whatever that means for the show's target generation.

See also: Magical Girl, Action Girl, Cute Bruiser. Plucky Girl is the 'non-superpowered, but gets the job done anyway' version. Not to be confused with a girl with an extraordinary amount of the Most Common Superpower.

Anime and Manga

 * This would probably be the best niche for Nodoka in Mahou Sensei Negima. While she and her best friend Yue are both learning magic, Yue seems to be gravitating more towards the magical artillery side of the scale, plus being a strategist. Nodoka, in comparison, has no real talent for magic, but she does know some. She functions as the group telepath/spy and is incapable of reaching the real level of Action Girl that the likes of Setsuna and Yue (post training as a magic knight) have. As such, her CMOA is limited to.
 * Arguably, Ayukawa Madoka from Kimagure Orange Road She can beat up five times her mass in delinquent thugs, gets straight As while skipping classes regularly, can play three instrument (Guitar, Saxophone, Piano) at professional, concert level, Surfed a 30 foot wave the first day she EVER surfed at all, and skateboarded down a building under construction in the middle of a snowstorm. She's more than a match for Kasuga, who is a powerful telekinetic.
 * Haruko from FLCL. She's from outer space, wields a gasoline-powered Rickenbacker bass guitar as a weapon, and plays baseball improbably well.
 * Mikura from Mezzo Forte supplements her un-paralleled hand-to-hand fighting and weapon skills with a touch of Psychic Powers: at times she is able to gain mysterious glimpses into the future. The same also applies to.
 * Tsunade and Sakura from Naruto for a while, until they were reduced to Faux Action Girl status (or in Sakura's case, back to Faux Action Girl status.)
 * The girls from Windy Tales with their Wind Manipulation powers.

Comic Books

 * Since Empowered's suit doesn't always work well, she has to think up other ways of defeating supervillains. Like ramming them with an SUV going 70 miles per hour.

Literature

 * Sometimes trouser-wearing Alice of The Witch Watch can summon fire, but the process is incredibly draining and will lead to her fainting after two or three attempts, so she normally ends up having to rely on her brains or on her little gun.

Live Action Television

 * One of the earliest EEGs was Evie Garland from the 80s Sitcom Out of This World, who derived her extraordinary powers from her half-alien heritage.
 * Similarly, Ta'ra from the short lived series Something Is Out There.
 * Sabrina the Teenage Witch used a similar formula, substituting "witch" for "alien".
 * Joss Whedon has admitted to having a thing for this trope, noting after Firefly that he "can't seem to create a show without an adolescent girl with superpowers" in it.
 * The title character of Buffy the Vampire Slayer, Whedon's most well-known TV creation, for instance, was one of the most notable instances on TV of this Archetype.
 * However, she's by far not the last Whedon character to fit the trope: in addition to other Slayers seen throughout the Buffyverse (especially but not exclusively in the comics, such as Fray or Buffy Season Eight), there's also psychic Waif Fu user River Tam from his shorter-lived cult hit Firefly.
 * He "has a thing" to the point that his Astonishing X-Men run actually regressed Kitty Pryde - in both age and personality - from the mature, confident woman she'd become in Excalibur, back to an EEG.
 * He also wrote an arc of Runaways. Admittedly, the EEG characters weren't his creation (except the two he added), but we're pretty sure they're the reason he likes that comic enough to write it anyway.
 * Even non-Slayer women in the Buffyverse may end up as EEGs. Case in point: Willow, most of the time. She took a trip to "super" status on a few occasions.
 * Max of Dark Angel.
 * All the main characters of Birds of Prey.
 * Alex Mack.

Web Original

 * RWBY: Most every female in the cast, in one way or another.

Western Animation

 * The title character of The Life and Times of Juniper Lee.
 * Arguably, most of the ladies from Avatar: The Last Airbender, but Mai, Ty Lee, and Suki in particular.