Girl-Powered

It's not easy being The Chick and Action Girl at the same time, you are often the target of being attacked by the bad guys and having next to no self-defense ability. And then there are the times where the only thing between the world being destroyed is you and possibly the magical McGuffin that allows only a girl to transform or let them use the item.

Who knows why the device won't work for guys, a slight technical oversight perhaps, maybe because it runs on certain sources of energy? But who knows. The Girl-Powered device ain't going to work on men at all, for some reason, and no attempt is made to get it to do so.

A very common thing in series with strong Les Yay and Yuri undertones.

See Virgin Power when not only is being a girl a requirement to use said powers, but she must also stay relatively chaste.

See Stay in the Kitchen for when Action Girls should stay away from combat.

Examples of Girl-Powered include:

Anime and Manga

The Humongous Mecha of the Alternate Universe in Parallel Trouble Adventure Dual only work for girls, with the execption of Kazuki. The reason Kazuki can is because his parallel twin is a Mecha. The reason why only girls can pilot the Mecha is that a limiter that was put in place, because men could make them produce Light Hawk Wings, which makes this an inversion.
Only girls can be Sailor Senshi, end of story. Tuxedo Kamen is the closest the series has to a male Sailor and represents Earth in the lineup, but his power comes from the Golden Crystal, the counterpart to the Silver Crystal, not a Sailor Crystal like the rest of the Senshi. This is what justifies the idea of Sailor Earth.
Only girls can become magical, well, girls, in Puella Magi Madoka Magica. There's no specific reason why there couldn't be a magical boy, but Kyubey and the rest of his alien race specifically target pubescent girls because their emotional output is much higher than any other human demographic; it's just not worth the investment for them to try to harvest anyone else.
Valkyria Chronicles has the Valkyria, who seem to be a race of only women. Men don't even bother picking up Ragnite lances as weapons.
- Then came the Valkyrie power armors which evened out the playing field, as well as other projects which gave them One Winged Angel forms, at the cost of their sanity.
The priestesses of the Fushigi Yuugi stories are, as the name implies, all female, for no other reason than the four gods just aren't into guys. Most of the Seishi are men, however.
Name a Comic Valkyrie Manga such as Freezing for example, the Pandoras (aka girls) are the actual combatants in the Battle Couple, the guys only purpose is to hold the bad guys down to allow the girls to beat them up
My-HiME and Mai-Otome, only a girl (and in Mai-Otome, a virgin) can have a CHILD. This doesn't stop Yuuichi from trying to help out, nor Mashiro (in the Manga, where she is really a he) pulling a CMOA in the end.
In VITA Sexualis, Shirou acts a conduit for allowing the already powerful female cast to transform and fight.
Strike Witches is a subversion as non-magical weapons can damage the Neuroi, but because it takes longer and more ammo to kill them, Witches are needed to quickly finish them off.
The titular Infinite Stratos combat exoskeletons are only usable by women, with the sole exception of the main male protagonist. Apparently according to the inventor, this wasn't intentional, but she won't care to fix this, nor find out why the main character can use it despite his gender.
Kämpfer, all the fighters are female and the only one who isn't goes through a Gender Bender to do so.
- Justified because the person distributing all of the Entrails Animals that make Kämpfers is Kaede and she's not interested in boys at all.
Gender inverted in D.N.Angel since only males can bear the "Dark" gene that allows them to take on their magical boy form.

Film

The McGuffin in the Red Sonja film could only be handled by women. Men who touched it were instantly killed by bad special effects.
Questionably present in Gunslinger Girl. It's explained that only children can be turned into cyborg, and never explicitly stated that they have to be girls, but we never see any sign of a male cyborg.
While the actual handlers in Asura Cryin can be of either gender. The Burial Doll are always girls.

Video Games

All Pegasus Knights in the Fire Emblem games are female, presumably because the Pegasi themselves won't allow men to pilot them. Wyverns, on the other hand, don't appear to be so picky, as there are Wyvern Riders of both sexes throughout the series.

Western Animation

The Heart of Candracar in WITCH allows a team of five Magical Girls to transform into Guardians to fight evil on Earth and in other universes. From what we've seen so far it's pretty much understood that only females are allowed to become Guardians for whatever reason, though the creator of the Heart was female in the comics and show and some fans speculate that this is the reason for the girls-only clause. The simpler explanation may be that WITCH is marketed as a girls' property and each of the Guardians are meant to relate to their audience.